the potential economic growth in the united states

86th Congress2d Session J JOINT COMMITTE:E PRINT

STUDY PAPER NO. 20

THE POTENTIAL ECONOMIC GROWTHIN THE UNITED STATES

BY

JAMES W. KNOWLES

WITH THE ASSISTANCE OF

CHARLES B. WARDEN, Jr.

MATERIALS PREPARED IN CONNECTION WITH THE

STUDY OF EMPLOYMENT, GROWTH, ANDPRICE LEVELS

FOR CONSIDERATION BY THE

JOINT ECONOMIC COMMITTEECONGRESS OF THE UNITED STATES

JANUARY

Printed for the use of the Joint Economic Committee

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JOINT ECONOMIC COMMITTEE(Created pursuant to sec. 5(a) of Public Law 304, 70th Cong.)

PAUL H. DOUGLAS, Illinois, ChairmanWRIGHT PATMAN, Texas, Vice Chairman

SENATE HOUSE OF REPRESENTATIVES

JOHN SPARKMAN, Alabama RICHARD BOLLING, MissouriJ. WILLIAM FULBRIGHT, Arkansas HALE BOGGS, LouisianaJOSEPH C. O'MAHONEY, Wyoming HENRY S. REUSS, WisconsinJOHN F. KENNEDY, Massachusetts FRANK M. COFFIN, MainePRESCOTT BUSH, Connecticut THOMAS B. CURTIS, MissouriJOHN MARSHALL BUTLER, Maryland CLARENCE E. KILBURN, New YorkJACOB K. JAVITS, New York WILLIAM B. WIDNALL, New Jersey

STUDY OF ElIPLOYMENT, GROWTEI, AND PRICE LEVELS

(Pursuant to S. Con. Res. 13, 86tb Cong., tst sess.)

OTTO ECySTEIN, Technical DirectorJouN W. LEHMAN, Adminietrative Officer

JAMES W. KNOWLES, Special Economic Counsel

11

This is one of a series of papers being prepared for consider-ation by the Joint Economic Committee in connection withits Study of Employment, Growth, and Price Levels. Thecommittee and the committee staff neither approve nor dis-approve of the findings of the individual authors.

inI

LETTERS OF TRANSMITTAL

JANUARY 12, 1960.To Members of the Joint Economic Committee:

Submitted herewith for the consideration of the members of theJoint Economic Committee and others is a paper on "The PotentialEconomic Growth in the United States."

This is one of a number of subjects which the Joint Economic Com-mittee requested individual scholars to examine and report on inconnection with the committee's study of "Employment, Growth, andPrice Levels."

The findings are entirely those of the author, and the committee andthe committee staff indicate neither approval nor disapproval of this

publication. PAUL H. DOUGLAS,

Chairman, Joint Economic Committee.

JANUARY 10, 1960.Hon. PAUL H. DOUGLAS,Chairman, Joint Economic Committee,U.S. Senate, Washington, D.C.

DEAR SENATOR DOUGLAS: Transmitted herewith is one of a seriesof papers prepared for the study of "Employment, Growth, and PriceLevels" by outside consultants and members of the staff. Theauthor of this paper is James W. Knowles, Special Economic Counselof the Study.

All papers are presented as prepared by the authors.OTTO ECKSTEIN,

Technical Director,Study of Employment, Growth, and Price Levels.

V

CONTENTS

PART IPage.

Chapter I. The nature and significance of potential economic growth- 1The Employment Act goals- 2A dynamic economy - 4Economic growth - 4Current economic performance - 5Potential output versus capacity_- 6The rate of employment- 8The measurement of potential growth- 9

Chapter II. The determinants of potential economic growth -iSupply, demand, growth, and output -_ 11Capacity and growth -12The production function -13Production in the individual plant versus the total economy … _ 13The design of an aggregate production function -16

Chapter III. The statistical analysis of output -19The variables and their measurement -19Three transformations -22Fitting the production function to the historical data -28The final equation- 31Interpreting the production function in economic terms -33Potential output: 1909-60- - ___-- __---_-_-_-_-___-_-_-_-_ 35

Chapter IV. Potential growth: Prospects and problems -38Alternative assumptions: 1959-75 -38The alternative projections -40Implications of the projections ----- ----- 43

PART IITechnical materials ------------------------ 45

CHARTS

Chart I. Capacity, output, and potential-an explanatory sketch- 6Chart II. Computed gross stocks of business plant and equipment at con-

stant (1959) prices (ratio scale) -21Chart III. Estimated percentages of original installations of plant and

equipment surviving after the periods indicated -22Chart IV. Gross national product in constant dollars and related variables,

1909-58 ------- 24Chart V. Gross national product in constant dollars, 1909-58, actual versus

predicted -32Chart VI. Potential gross national product compared to actual 1909-59,

and projected for 1975 - 36

TABLES

Table 1. The variables used in the anslysis, and their components, 1909-58- 26Table 2. Actual, predicted, and potential gross national product in 1954

dollars for the United States, 1909-60- - _- __- ___-___-_-_------ 37Table 3. Selected indicators of economic growth potentials -40

VII

STUDY PAPER NO. 20

THE POTENTIAL ECONOMIC GROWTH IN THEUNITED STATES1

PART I

CHAPTER I. THE NATURE AND SIGNIFICANCE OF POTENTIAL ECONOMICGROWTH 2

Confidence in the Nation's potential for future economic growthhas been the fundamental assumption upon which public and privateeconomic policies have been based in the United States since itsfounding. Though occasionally challenged during unexpected re-verses, as during the 1930's when concepts of economic maturity andstagnation were brought into the debates over economic policies for atime, this basic belief in the possibilities or opportunities for futureincreases in employment, output, and in per capita, real purchasingpower for a rising population, has survived all vicissitudes of publicdebate to provide the foundation for public and private economicpolicies.

Hamilton's "Report on the Subject of Manufactures," 1791; en-couragement to canal building; public lands policies; land grants toencourage railroad building beyond the limits of settlement; "Mani-fest Destiny;" aid to agricultural and mechanical education, includingcolleges; the "New Era;" the patent system-any student of Americaneconomic history could compile a long list of examples of growth-oriented policies and programs in both the public and private sectorsof the economy. In 1812, when the population was less than 10 inil-lion, a sketch of the Nation's destiny pointed to an economy of 100million, stretching from Atlantic to Pacific, possessed of large cities,magnificent canals and roads, seminaries of learning, vast domesticmanufacturing industries, and other advantages of division of labor.(1) In 1872, when the population was hardly 40 million, another writerforesaw a population of 300 million, mail delivery from coast to coastin 24 hours, artificial fibers, and expansion of steel production by over50 times (incidentally a drastic underestimation) (2).

1 I wish to express my deep appreciation to my research associate in this study, Ir. Charles B. Warden,Yr., who carried the burden of preparing the various time series for use in the study and brought together thematerial on potential labor force and hours of work. Without his careful and unstinting efforts, the studycould not have been brought to completion.

Mr. Thomas Wilson of the special study staff gave invaluable assistance in carrying out the complex com-putations on the IBM 650 computer. We are especially grateful to the Bureau of Labor Statisties and the

oard of Governors of the Federal Reserve System, who made time available on their IBM 650 computersso that we could carry out these computations.

'Numbered references tn parentheses in text are to numbered sections of "Technical Materials,"beginning on p. 45.

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2 POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

The Employment Act goalsWhen the Employment Act of 1946 incorporated economic growth

as an objective of national economic policy, therefore, the action wasin line with a long American tradition. The emphasis on maximumor full employment in the early history of the act, both before andafter enactment into law, occasionally has led to the comment thatrecent stress on economic growth and price stability as objectives ofpolicy constitutes a change in interpretation of the act's stated goalsof "maximum employment, production, and purchasing power" (3).

The act's language and history yield a different view. Section 2declared it is to be "* * * the continuing policy and responsibilityof the Federal Government to use all practicable means * * * topromote maximum employment, production, and purchasing power,"with maximum employment clearly stated to involve " * * creatingand maintaining * * * conditions under which there will be affordeduseful employment opportunities, including self-employment, for thoseable, willing, and seeking to work," and, further, these objectivesshould be accomplished through programs which would " * * fosterand promote free competitive enterprise and the general welfare" (4).

The Employment Act, it should be noted, does not purport toguarantee or assure full employment, an adequate rate of growth, anda stable level of prices. It does commit the Federal Government, incooperation with other public and private agencies, to "* * * utilizeall its plans, functions, and resources" to promote the accomplishmentof these objectives.

The Employment Act, as basic enduring statutory law, is generalin its statement of these goals or objectives, but it seems clear fromthe legislative history that supporters of the act did not intend itsgeneralized expression of ultinate or ideal aspirations of a free peopleto be empty phrases or mere timeless expressions of vague hopes. Infact, under the act, the President is required to submit to the Congressat the beginning of each of its regular sessions an Economic Reportwhich shall set forth " * * the levels of employment, production,and purchasing power obtaining in the United States and such levelsneeded to carry out the policy [sec. 2] * * *." Prediction of thefuture course of the economy in specific quantitative terms was notrequired, according to one interpretation of section 3(a), though theact does direct that the Economic Report contain a statement of"* * * current and foreseeable trends in the levels of employment,production, and purchasing power * * * There is an unmistak-able mandate, however, for the regular, annual administrative deter-mination of the levels of activity which will give definite and timelymeaning to the ideals expressed in section 2 of the act (5).

This annual determination of the specific employment, output, andprice levels which would constitute, in the judgment of the Presidentand his advisers, the optimum achievement of the economy for theparticular year requires the development of estimates of the economy'spotentials for employment, growth, and price performance. Suchquantitative economic potentials provide guidelines with which theactual performance of the economy can be compared, revealingdirections and magnitudes of improvements needed if nationaleconomic objectives are to be achieved.

When estimates of the economy's potential employment and outputare computed, however, the result necessarily constitutes measures of

POTENTIAL ECONO-MIC GROWTH IN THE UNITED STATES 3

potential growth of the United States. In a country with an increas-ing population, sufficient savings, and a significant rate of techno-logical advance, maximum employment and output, if achieved yearafter year, will be accompanied by growth-the increase in populationmakes possible a rising supply of labor; saving makes possible a risingstock of capital; and technological progress results in labor and capitalbecoming more efficient so output rises even faster than population.Obviously this is not an inevitable set of relations at all times in allcountries but the combination has been true in this country.

The connection between maximum employment and production,on the one hand, and potential growth on the other, was recognizedeven during the debates preceding passage of the Employment Act.A number of projections were prepared providing estimates of thegrowth of employment and output which might reasonably be expectedin the immediate postwar years in view of past trends and then knownconditions (6). The early Economic Reports contained similar esti-mates of the possible employment and output which could be achievedif recession were avoided (7). Beginning in 1950, its staff has pre-pared similar estimates for the use of the Joint Economic Committee,estimates to which the label "potential" growth has been applied sincepublication of a staff study in 1954, entitled "Potential EconomicGrowth of the United States During the Next Decade" (8).

In the same way that economic growth possibilities have been aninseparable part of the Employment Act's history and of the goals setforth in section 2, the ideal of a stable level of prices has always beena basic part of the act. It is easy to understand why this point shouldbe the subject of controversy since the act treats of price stabilitysolely through its reference to maximum purchasing power. Thisterm has generally been taken to imply a stable level of prices sinceadvancing prices clearly erode the purchasing power of both currentincomes and past savings (9). But the failure of Congress to delineateclearly the kind of price behavior to be sought under the act provideda basis for controversy.

From the beginning, the President's Economic Reports, statementsof his Council of Economic Advisers, and the activities and reports ofthe Joint Economic Committee have reflected deep concern about theinflationary tendencies of the postwar period. President Truman'sfirst Economic Report under the act (January 1947) pointed to therise in prices in the latter half of 1946 as an impediment to the maxi-mum purchasing power goal of the act. The Joint Economic Com-mittee in June and July 1947 devoted its first major inquiry to pricedevelopments. Whatever may be one's view as to the desirability ofchanges in the language of the act, one point is indisputable-those inthe Federal Government charged with the responsibility for policyunder the act have always operated on the belief that reasonableprice stability is one of the objectives it sets for national economicpolicies (10).

This study of the potential economic growth of the United States,therefore, is the latest in a series of quantitative analyses of economicgrowth possibilities which have originated in connection with theEmployment Act. It differs in some respects from its predecessors,however, and succeeding chapters can be more easily followed if theconcept of economic growth, its relationship to policy analysis under


the Employment Act, and the analytical framework used in developingthe estimates of potential growth are sketched briefly at the outset.

In line with the preceding discussion, this study looks at the goalsof maximum employment, production, and purchasing power as direct-ing attention of public and private policymakers to the ideal of adynamic, growing economy, exhibiting a minimum of fluctuation inactual rates of use of labor and capital around the maximum averagerate of utilization feasible under existing institutional conditions,which, at the same time, is consistent with reasonable stability ofthe general average level of prices of goods and services.

A dynamic economyThe "dynamic" aspect of this ideal seems to have been reflected in

the act, though not perhaps in the exact language an economist mightsuggest if it were being drafted today. The goal of a free, private,competitive economy, listed in section 2, calls for a dynamic economy,i.e., one free from those public and private restraints which wouldimpede adjustment to changes-

(a) in individual tastes and preferences;(b) in effective demand for different goods and services as a

result of (a) above combined with changes in the level and distri-bution of purchasing power, and changes in relative prices;

(c) in techniques for combining resources in production;(d) in characteristics of products and services;(e) in the geographic distribution of population and industries;

and(f) in international economic relationships.

"Dynamic" thus describes the more outstanding characteristics-ofAmerican economic life. The frequency and magnitude of thesechanges have a profound effect on the potential rate of economicgrowth, on the magnitude of the frictions in the economy and henceon the proportion of resources which are unavoidably idle at any giventime, and on the ease or difficulty faced in minimizing economicfluctuations.Economic growth

Economic growth is an increase in the Nation's capacity to producegoods, services, and leisure (11). It is not, therefore, synonymouswith the idea of progress or with the more conventional concept ofeconomic growth as an expansion of real per capita gross nationalproduct, or with other definitions of growth that have been used fromtime to time. The distinction between progress and economic growthis the familiar distinction economists make between means and ends.Progress relates to an increase in the welfare of the people of theNation while economic growth is an increase in the economy's produc-tive capacity, i.e., an increase in the Nation's ability to provide thematerial means to satisfy individual or collective desires for differentkinds of goods and services, and thus, in the end, contribute to anincrease in welfare. Much of the increase in well-being-progress-comes about in ways unrelated, or only indirectly related, to economicgrowth, per se, such as: a decline in the death rate; a rise in the per-centage of children of school age in school and of youths going on tohigher education; the growth of leisure; the growth of the creativearts; the circulation of books; a rise in political and religious freedomfor the individual; improvements in moral standards and behavior.

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES 5

Economic growth as an objective of national economic policy,therefore, is an intermediate objective-it is a goal which the Nationcan seek in order to provide a material basis for progress or an increasein welfare. If the output of goods and services that results from theincreased productive capacity of the economy is used wisely, and inaccordance with the desires of individuals and of the community asexpressed through community and political channels, it can contributeto welfare and progress. Professor Galbraith has produced perhapsthe most familiar recent example of an economic analysis resting onthe distinction between progress and growth in capacity to providematerial goods and services (12).

Distinction between economic growth and a mere increase in output,either in the aggregate or per capita, is of both practical and theoreticalsignificance. The distinction is between the performance of theeconomy in any given period of time (output, or increase in output, forexample) and its capability. Economic growth refers, of course, toan increase in the capability or productive capacity of the economywhile the current performance of the economy is measured by output,employment, the increase in output, output per capita, real income percapita, the amount of leisure (individual), and the stability or in-stability of output, employment, and prices.

Current economic performancePerformance of the economy is reflected in the Employment Act's

description of the other aspects of its ideal of how the economy shouldoperate. As stated above, this means at least the following: (1)a minimum of fluctuations in actual rates of use of labor and capitalaround the maximum average rate of utilization feasible under existinginstitutional conditions, managerial skill, and economic knowledge;and (2) reasonable stability of the general level of prices of goods andservices.

The first part of this definition of economic performance is generallycalled economic stability for it means that there is a limited range offluctuations in the rate at which the Nation uses its economic capacity,human and material. It therefore implies a constantly rising levelof employment and of total production of goods and services as theNation's supply of labor and capital goods increases. In the Em-ployment Act this stability objective, in part, is described as maximumemployment and production, referring to that aspect of economicstability which I have just described.

It also includes, of course, the second aspect already noted, stabilityin the general level of prices of goods and services. In respect to thisgoal, it is necessary to refer to the fact that the economy should bedynamic, adjusting readily, rapidly, to changing conditions. In suchan economy, relative prices must remain free to change, that is eachindividual price, or the prices of individual goods and services, mustbe free to change rapidly and in such magnitude as will call forth thosechanges in outputs, demands, and resource allocations required bychanging preferences, incomes, and technological feasibilities. Pricestability implies that while the general average of prices is reasonablystable, with no upward or downward drift, each individual priceremains free to change relative to the general level so long as thevarious changes offset each other and leave the general averageunchanged.

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

Potential output versus capacityAt the outset of this chapter, the term "potential" was used and

reference was made to the Nation's potential for economic growth.Now we refer to economic growth in terms of an increase in theNation's capacity to produce goods and services as well as leisure.

In the analysis that follows, the distinction between capacity andthe output potential for which a measure is developed, is of criticalimportance. To make the relationship clear, chartI was developed.

CHART I

CAPACITY, OUTPUT, AND POTENTIALan EXPLANATORY SKETCH

- Capacity

Percent Potential200

Zone of unavoidable/ _~~~~~~~~ , ~~~minimum variation

50 ActualOutput

I I I IYear I Year 2 Year 3 Year 4 Year S

It will be noted that the topmost line, labeled "capacity," is abovethe "potential" by some unspecified percentage, though the two linesare shown parallel. The potential is a measure of the optimum orbest practice which it is believed the economy is capable of sustainingon the average, year after year, without running into serious insta-bility of employment, output, or prices. It is, in a word, a measureof what would be reasonably good performance of the economy, main-taining a stable relationship between output and capacity. Aroundthis line of potential, lines have been dotted which represent whatmay be termed tolerance zones. Within these limits, the economyis fluctuating by so little that it cannot be regarded as being a seriouschallenge to the objectives of the Employment Act though certainlya matter of concern. Over time, it might be possible to reduce thistype of variation. In fact, one of the objectives of economic research,both pure and applied, should be to determine what these limits ofvariation are and how much they can be narrowed in practice.

No attempt to determine them quantitatively has been made inthis study.

6


Actual output is shown varying part of the time within this ac-ceptable zone on either side of the potential, sometimes above andsometimes below. Occasionally, output may move completely out-side of this tolerance zone. Either it rises too close to capacity,hence, into a seriously inflationary and probably unstable position, or,on the other hand, falls far below the potential as recession and wide-spread unemployment develop. In terms of the objectives of theEmployment Act, the stability goal would be achieved if the economycould remain inside the zone of acceptable variations, as close aspractical to the potential line. Over time, to the extent possible, anincrease in the ratio of potential output to capacity would be desirableso long as this does not involve either inflation or drastic instabilityof output and employment. As a practical matter, therefore, themeasurement of the potential output of the economy can be animportant instrument for analyzing the relation of current economicperformance to the objectives of the Employment Act, that is, as towhether or not output and employment are staving as close as reason-able men might require to the standard set up by the Employment Act.It also may be used as a convenient technique for analyzing thecurrent situation of the economy a use to which, in fact, the staff ofthe Joint Economic Committee has been putting earlier versions.

If an index of capacity for the total economy was available, theproblem would reduce to two steps: (1) Analysis of causes of growth ofcapacity; and (2) analysis of operating characteristics of the economyto discover the optimum operating rates, or ratio of output to capacity.But, economic analysts have debated at length whether or not it ispossible to develop an unambiguous concept of capacity for theeconomy (or even a single industry), much less measure it. To illus-trate the point, it may be possible to operate a given plant 24 hours aday, yet under ordinary circumstances the usual practice may be tooperate only one or two 8-hour shifts a clay. Suppose the plantordinarily operates on one 8-hour shift per day, what is the practicalcapacity of the plant? By this standard, capacity would be theamount produced in one 8-hour shift. Obviously, if demands werestrong enough it would be possible to operate the plant three shifts, or24 hours a day-tripling its capacity. Many plants that normallyoperated one shift or two shifts added shifts during World War II,and plants that normally operated on an around-the-clock, continuous-process basis were run during these war emergency years at increasedrates of output through such devices as lengthening the period betweenmaintenance or repair, thus reducing downtime.

In a host of ways, therefore, the maximum output of the economyis flexible over a considerable range, even when each industry or tradeis operating at what managements ordinarily would call full capacityrates. No attempt was made, therefore, to measure the ultimatecapacity of the economy. It is clear only that it must be much higherthan the measure of potential output arrived at in this study. Foreach year, the potential output level represents the amount the economycould produce at some stipulated rate of use of the labor force and ofcapital, and under the assumption that productive resources are usedat something approaching the economy's notion of a least-cost com-bination of inputs. That is, capacity, however conceived, is beingoperated so as to produce output at the least cost per unit of output, in


accordance with the best practices possible with existing management,capital, and training and knowledge of the labor force. It is, in a word,a measure of what practical man can do under the usual operatingconditions maintainable over long periods of time without excessstrain or breakdown, on the one hand, or, on the other, excessive,wasteful slack in the system, particularly prolonged, involuntary un-employment of labor.

The rate of employmentA key element in the measurement of the potential output is the

ratio of employment to the labor force, or, in more familiar form, thepercentage of the labor force unemployed. This ratio, the key todebate about Employment Act policies, never has been definedofficially, either by the executive branch, the Congress, or any of itscommittees. Indeed, no such definition could be stated which wouldbe valid for all time, because of two bas'c facts.

First, measures of employment, labor force, and unemployment,undergo improvements from time to time, with a consequent changein the level of unemployment revealed by the surveys and in the ratioto the labor force. The same degree of tightness in labor markets, forexample, might be measured at one time by, let us say, 3fi percent ofunemployment, whereas later under a different system of measurement,perhaps using an improved interviewing technique, an enlargement ofsample, or other change in the statistical program, the same degree oftightness might be measured by a figure which averaged 4 percent..Does this mean the percentage of unemployment has increased or ourobjectives have changed? Obviously not. The same degree of tight-ness or slack in the labor force is revealed each time. It is simply thatthe measuring device has changed and, presumably, is more efficientthan formerly. There is need to be aware constantly of changes or im-provements in the system of economic measurement, and, from timeto time, redefine, in terms of the changing system of measurements,maximum employment, production, and purchasing power within themeaning of the Employment Act (13).

The second point is that the Nation ought to, and does, strive con-'tinually to make improvements in the efficiency with which labormarkets operate and in the efficiency with which labor is used. Ifthe efficiency with which shifts'of labor from job to job and fromindustry to industry, is raised and the stability of the economy in-creased, then we should be able to operate with, let us say, only 3percent unemployment on the average compared to about 4 to 5percent unemployment, which seemed to have been achieved, in fact,on the average of the better years, simply because policies could notbe designed to do better consistently (14). One path of progress isthrough learning how to operate with less slack in the labor force-less time spent between jobs, unemployed because labor markets donot operate smoothly in transferring labor from places and industriesexperiencing declining demand to places and industries with increasingdemand.

Even if the efficiency of the economy increases, and the flexibilityand speed of operation of labor markets improves, the Nation may bewilling to tolerate or even seek a higher level of unemployment than

POTENTIAL ECONONUC GROWTH IN THE UNITED STATES 9

the minimum technically possible. This might happen if the unem-ployment was exceedingly short-range-that is, only a few days ora week or two at a time for each person affected-and constituteda necessary condition for achieving a desired speed of movement oflabor between industries, occupations, and jobs; in the process, pro-ducing a much-enlarged scope of opportunity for each individual toimprove himself, and a wider range of choice. In a word, althoughthere could be. a net gain in welfare or progress from a higher rateturnover of the labor force, this higher turnover itself-thoughdesirable-would generate a higher level of unemployment on theaverage (15).

While there has been no official statement or determination of thepercentage of the labor force unemployed which shall be regarded asconsistent with the objectives of the Employment Act, nevertheless,various figures have been widely used in discussions of policy underthe act. These figures range between 2 percent on the low side to5 or 6 percent unemployed in the upper end.of the range. The staffof the Joint Economic Committee has from time to.time computedthe output of the economy at an assumed rate of maximum employ-ment, or a potential growth trend, basing this computation on theassumption that unemployment would average about 4 percent ofthe civilian labor force (16). In periods of high. prosperity, withmodest fluctuations in output and employment, unemployment hasaveraged about 4 percent of the labor force.

In view of the historical record, and the past use of the 4 percentfigure by the staff, it is again used in this current study. In thediscussion below, chapter IV, it will be shown that the choice of anassumed rate of unemployment does have implications both forpublio.and private policies, and for the rate of growth. For thehistorical analysis in chapter III, however, the choice of any averagethat would seem reasonable for the past probably would result in apotential output close to that calculated on the assumption of 4percent actually used. While a lower rate than this could be achievedin the future if private and public policies were designed to do thejob, in the past the economy has not achieved a lower unemploymenton the average. It seems useless to measure past performanceagainst a standard the economy seems to have been unable to achievein view of its institutions and technical possibilities.

The measurement of potential growthHow can economic growth, in terms of the potential output as

described above, be measured?In the first place, the output measure to be used is the total of

goods and services in constant prices, that is, real gross nationalproduct. Potential output, then, is the real GNP that the economywould be capable of producing under stipulated assumptions, theprincipal one being that 96 percent of the labor force is employed.This is merely the indicator or measure.

How can the level of this indicator and its rate of growth becalculated? The potential output and growth of the economy de-pends on the amount and rate of growth of available resources andtheir productivities; in short, upon the size of the labor force, its

50506-60-3


skills and know-how, on the accumulated stock of capital, on theavailability of natural resources, and upon the current technologyand the rate at which new techniques are introduced.

These factors are familiar. Output and growth also are influencedby the rate and character of scientific research; the proportion of out-put which is plowed back into intangible capital assets; the extent towhich the current capital stock embodies the most up-to-date-tech-nology or still reflects that of some past period; rising levels of educa-tional attainment and health; the ratio of the labor force to population;changes in the average number of hours worked per year per personemployed; changes in the average degree of managerial skill; the degreeof stimulation of advancement of efficiency from competition at homeand abroad; and a wide variety of influences arising out of the socialand political environment in which the economy operates. Some ofthese factors cannot be measured directly at the present time, some ofthem are not measured though. perhaps they could be, and some maynot be measurable at all.

Economists, however, cannot put off attempts at the solution ofpractical problems until final, perfect solutions to the problems ofconcept and measurement can be found. Progress comes from thecontinual interplay of theory, measurement, and empirical analysisso that theorists develop better analytical tools out of the challengeof practical research attempts, while measurement and empirical anal-ysis progress by using to the utmost whatever tools are available todo the best job possible at the moment, recognizing always that even-tually some better solution will be possible when improved tools andimproved measurements are developed out of experience.

In this spirit, the present study is an attempt at development of asimple model or description of the economic process of production,using available measurements of the various inputs and outputs, andat development of a way of determining from these data the quan-titative relationships between the various inputs and outputs.

In chapter II, the technical argument is outlined, including themeasures of the various factors and the aggregate function, expressingthe relation between inputs of productive factors and outputs of goodsand services. Further, the structure of the model of the growth ofthe economy will be related to preceding work.

In chapter III, the actual fit of the model to the histor cal data isgiven, showing the way in which the actual relationships were de-veloped by processing various measures of inputs and outputs. Someof the implications of this analysis for interpreting past economicgrowth are developed.

In chapter IV, the measures of potential economic growth developedin chapter III are utilized to develop a picture of the possibilities forfuture potential economic growth of the United States to the year1975, with some discussion of their implications for public policy.

Notes referring to sources or expanding on particular technicalpoints in the analysis are given in part II of this paper, entitled"Technical Materials." Numbered references throughout part Iare to these numbered "Technical Materials."

CHAPTER II. THE DETERMINANTS OF POTENTIAL ECONOMIC GROWTH

The calculated growth potentials of the American economy pre-sented in chapters III and IV rest upon an analysis of the historicalrecord of the performance of the economy and of the major output-determining factors. Fortunately today the analysis of the factorswhich determine the output of the economy at any particular timeand which determine the rate at which the economy's capabilities forproducing goods and services increases over time, can draw upona much larger and richer body of theoretical and empirical researchthan formerly.

Almost two decades ago, when, during World War II, analysts inand out of Government developed models of the economic growthof the economy as a basis for making projections of a postwar fullemployment economy, the data available and the analytical toolswere more primitive than at present. These models, or projectionswere used to study the problems of reconversion and unemploymentwhich would arise when World War II came to an end, and a return tomore peaceful conditions was possible. In the intervening years, botheconomic theory and empirical research have turned increasingly to thestudy of economic growth and progress under various pressures ofpractical problems, on the one hand, and of increased theoreticalinterest on the other. This increased interest in, and devotion ofintellectual and research resources to, the study of economic growth isall to the good.

Professor Domar has stated the past position of growth in economictheory quite aptly:

In economic theory, growth has occupied an odd place: always seen around butseldom invited in. It has been either taken for granted or treated as an after-thought (17).

The turn of economic research toward mathematical and empiricalstudies, finding its ultimate expression in rationally designed econ-ometric studies and input and output tables, has produced a wholenew body of analytical tools for tackling the problems of analyzing andmeasuring the potential growth of the economy. The pioneering workis found in the studies of the production function and its empiricalmeasurement, by Prof. Paul H. Douglas and his colleagues, first atAmherst and later at the University of Chicago, which found expres-sion in the Cobb-Douglas production function (18).

This work has been carried forward in a number of studies includingthose by Tintner, IHildreth, Nichols, Verhaulst, Heady, Solow, andLeontief (19). Closely related developments have occurred in linearprograming (20) and the development of input-output models asso-ciated principally with the work of Leontief (21). The criticalliterature on the statistical derivation of production functions is ex-tensive, especially on the economic interpretation of the results (22).

Supply, demand, growth, and outputThe previous chapter stated that the growth in the economy's

capabilities for producing goods and services, that is, its capacity, and,11


hence, by implication its potential output, is a function of a largevariety of factors affecting the supply of productive resources-labor,capital, natural resources-as well as the efficiency with which thoseresources can be used in production. Actual output is a result of awide variety of factors affecting both demand and supply. The rateof increase in output will be determined by the growth of demand, onthe one hand, or the growth of supply, or potential output, on theother, according to which is the smaller, and hence the limiting factorin each period of time. If the potential growth is growing at 4 percentper year, and aggregate demand is growing at 3 percent, then, outputobviously will tend to be limited to a rate of rise of 3 percent ratherthan rising in line with the potential supply at 4 percent per year.

The reverse situation, of course, will be true if aggregate demand isgrowing at, say 5 percent, while the growth of potential output is only3 percent. In this case an inflationary excess of demand will developand the excess of aggregate money demand over potential output willfind expression in inflation-a familiar development during war periodsor periods of monetary inflation.

In making an analysis of the historical record in search of a measureof potential output and growth, allowance must be made for the factthat two sets of forces have been operating-a set of demand factorsand a set of supply factors that tend to make available output in linewith demand. In the analysis, therefore, measures of cyclical varia-tions in demand and other short-term influences have been introducedand by taking account of these, the output of the economy at somerate of operation, which we shall specify as the potential, was deter-mined for each year, defining this potential in terms of a rate of useof resources. The historical data analyzed below cover the years 1909to 1958 in detail.Capacity and growth

The preliminary sketch presented in chapter I (p. 6) indicated onepossible approach to analyzing and measuring the potential output ofthe American economy and its rate of growth. If, in addition to theseries on GNP in constant prices, a measure of capacity was available, itwould be possible to calculate the ratio between actual output andcapacity for each year, or month, or quarter, over a series of years.Then the performance of the economy in each of these time periodscould be studied and compared with the ratio of output to capacity.From this process, it would be possible to arrive at an average ratio ofoutput to capacity corresponding to criteria for desirable perform-ance, including perhaps ratio of employment to the available laborsupply, use of capital to availability of capital, stability of prices, andrate of growth of capacity. This average ratio applied to themeasure of capacity each year would give a time series representingthe desired potential output of the economy.

This would be a suitable process if a reasonably unambiguousmeasure of the capacity of the economy was available. As notedabove, no such measure for the capacity of the economy as a wholeis available and, indeed, there is much dispute ovef whether or notone can be produced, or even designed in theory (23)..' The problemof computing the measure of potential economic growth arises in partbecause the development of a concept and measure of the capacityof the economy has proved impossible up to the present. -


The production functionIf the problem cannot be approached via a measure of capacity,

how can the definition and measurement of the potential output bearrived at more directly from an analysis of the historical record ofthe performance of the economy?

The technique used involves a variation on the economists' deviceof "the production function." By this is meant a set of functionalrelationships between each of the productive factors and the outputof the economy. As noted above, output is the aggregate of theeconomy-including government, agriculture, all of the various otherprivate industries, nonprofit organizations, individual households,distribution, finance, and services-in a word, all that is covered inthe now conventional measure of output, the gross national product.This measure is used here in real terms adjusted to constant 1954dollars.

In the past, production functions have been developed coveringmanufacturing (24), agriculture (25), and for somewhat larger aggre-gates (26). An extensive literature has developed on the theory ofproduction functions and the interpretation of the results of fittingthem to statistical data for individual industries, sectors or the econ-omy as a whole (27). Since the economy is made up of literallyhundreds, if not thousands, of industries or separate economic sectors,of several million business firms, at least a minimum of 100,000governmental units, and somewhere in the neighborhood of 55 to60 million household units, as well as numerous foreign entitieshaving an impact on our economy, the process of deriving a mean-ingful aggregate production function involves heroic simplifica-tions. Any attempt at aggregate or national economic analysis in-evitably faces this problem, which, in the literature, has led to elabo-rate investigations of theories of aggregation and the construction ofindex numbers.

While these problems in aggregation and index number construc-tion are not discussed here at length, it must be recognized at theoutset that existing measures of total output and inputs are com-promises arrived at in the search for the best measures possible atthe present time. The question to be answered is whether or notthe utility of such devices of aggregate analysis is sufficiently greatto offset any lack of precision such compromises entail. This studyis founded on the conviction that the price is not too great-thatuseful analyses of the economy as a whole can be made if the qualifi-cations arising from aggregation are kept constantly in mind.

Production in the individual plant versus the total economyThe characteristics of the aggregate production function for the

economy developed below will be clearer if its relationship to theproductive process in an individual plant is outlined briefly. In sucha small unit-small compared to the total economy-productionconsists of a series of processes of combining and coordinating ma-terials, forces, services in the creation of valuable goods or services.These valuable goods or services are called output, while the materials,forces,:and services used up in their creation are called inputs. Theseterms have different meaning in the case of the individual establish-ment than when used with reference to the economy as a whole. In theindividual case, a good or service can be an output of one establish-ment but an input'to another. In' aggregate output, measured by


GNP, only the value added in each establishment or firm is counted,costs of purchased materials being deducted, so that total output is asfree as possible of double counting. The total of the incomes paid toproductive factors will equal total output for the economy as a wholebut will fall short for the individual productive unit by the value ofpurchased materials and components.

A second distinction exists between the flows per unit of time-year,month, etc.-of inputs and outputs, on the one band, and stocks ofgoods or productive resources on the other. Generally, inputs andoutputs are time flows, such as hours of labor or of machine time onthe input side of the productive process, and tons of steel per yearor months of rent of dwellings on the output side. Stocks are sourcesof flows of productive services-capital and labor-and are results ofpast output flows, being the sums (integrals) of those parts of pastoutput flows which were not used up, consumed, in the time periodin which they were produced.

The production function relates the flow of outputs per unit of timeto the various flows of inputs per unit of time in such fashion that ifthe coefficients of the function are known, and the volumes of thevarious inputs are known, the resulting volume of output can be pre-dicted from the function.

The third important distinction is between production under sta-tionary or static and under dynamic conditions. A static situationmay be thought of as one in which productive capacity is unchangingand technical knowledge always remains the same. Under these con-ditions, met with occasionally in an individual unit, but rarely, if ever,in an entire economy, the volume of production can vary only betweenzero and the fixed capacity volume, and the constant knowledge oftechnical possibilities readily yield the best combination of productiveresources to yield any required output volume between these limits.

In a dynamic situation, capacity can be expanded to meet demandsas they push beyond present capabilities, present inputs may increaseeither current output, as in the static case or future outputs, and tech-nical knowledge can change, making possible combinations of produc-tive services or types of outputs not previously feasible. In a dynamicworld, current output possibilities and the spectrum of input combina-tions reflect the cumulative effects of an endless stream of past deci-sions allocating resources between consumption and investment, andbetween investment in tangible productive resources and in intangiblessuch as education, research, health, institutional arrangements (pro-tection of competition, economic and political rights at law, etc.) andpromotion of moral standards.

. To bring out the implications of these distinctions for the lateranalysis, let us assume a productive unit with a fixed stock of plantand equipment, operating in competitive markets for both inputs andoutputs, and during a time period in which technical knowledge isunchanged. At low rates of production, output will tend to rise fasterthan inputs, productivity will rise as volume rises and the firm willexperience increasing returns. At higher operating ranges, output andinputs will rise together, the rise in productivity will slow down andfinally halt so that constant returns appear. If very high rates ofproduction are attempted, productivity may fall and decreasing re-turns set in as inputs rise faster than output.


What happens if dynamic conditions replace the static assumptionsused above? First, capacity ean now change as a result of investmentin new plant and equipment called forth by high rates of productionand high profits. The same type of relationship between inputs andoutputs will prevail as in the static case at each point of time but atthe larger volumes corresponding to rates of utilization of productiveresources experienced at the former lower capacity.

Changes in techniques are also possible and these have a somewhatdifferent range of possible effects. One possibility is that changeswill be neutral as between inputs so that production relations retainthe same shapes but the efficiency of each combination of inputs isincreased-that is, a doubling of capital and labor inputs which woulddouble output under one set of production relations, might, throughsimultaneous changes in techniques, be accompanied by a tripling ofoutput.

It will be noted that under both static and dynamic conditionssome combination of inputs is feasible which, given existing tech-niques, relative prices and stocks of productive resources, yields aminimum total cost per unit-that is, a least-cost combination. Arational entrepreneur would prefer to maintain this rate of output atall times if this were possible. Little is known about the rates ofproduction corresponding to these least cost combinations, but suchinformation as is available suggests that this rate is below what man-agement generally regards as the practical capacity of their firms,particularly in manufacturing.

The McGraw-Hill surveys of business plans for investment in newplant and equipment provide estimates of actual operating rates and ofpreferred operating rates in various manufacturing industries. Thissurvey measures capacity in terms of plant and equipment withoutadjustment for availability of manpower or materials. Each companyreports changes in capacity and rates of operation in accordance withtheir own definition though most companies in each industry appearto follow similar practices in defining capacity. In two surveys (1955and 1957) companies reported their preferred operating rates. Forall manufacturing, the preferred rate is reported to be about 90 per-cent of capacity and the rates for individual industries range from85 percent in transportation equipment to 95 percent in paper and 96percent in steel.

If, in general, managements tend to report as preferred operatingrates, those corresponding to their least-cost combination of resources,as seems reasonable, then it could be concluded that the optimumoperating rate, at least in manufacturing, is significantly below man-agement's estimate of practical capacity and even further below anyconceivable measure of absolute capacity since this must be well aboverated capacity. Higher rates of operation for prolonged periods (asduring and immediately after World War II) amply sustain this point.

When attention turns from the individual plant, firm, or industry toan aggregate production process for the total economy these pointsbecome clear:

(1) The optimum or best operating rate for the economy may notbe a simple average of the preferred or optimum rates of the individualproduction units-firms, plants, etc., weighted by their individualcapacities. The optimum rate for the total economy will reflect boththe individual preferred rates and the composition or mix of demand


which may not call for operations to be at the optimum or preferredrates in each individual producing unit. Under dynamic conditions,some misjudgment of markets by firms is unavoidable and cannotquickly be corrected by shifting resources to other outputs.

(2) The optimum rate of operation for a dynamic economy such asours will be affected also by the proportion of labor and capital whichmust be shifted annually to new uses or retired in order to adjust tochanging demands and techniques. The higher the rate of turnoveror shifting of resources in response to dynamic changes in the economythe lower the optimum rate of use productive resources which it ispractical to aim for and vice versa.

(3) As a corollary to point'(2), the more mobile resources are, themore rapidly and efficiently they respond to changes, the higher thepreferred operating rate for the economy can be; while slow adjust-ments or shifts will lower the operating rate which can be on a sustainedbasis without inflation.

(4) For the total economy, it will be difficult to detect statisticallyvalid evidence of increasing or decreasing returns under dynamic condi-tions, except those associated with wide cyclical swings in the rates ofoperation-recession or deep contraction and subsequent recovery, onthe one hand, and periods of over-full demand, such as World War II,on the other. During other periods, the influence of technologicalprogress on productivity of resources, and inevitable errors in esti-mating'inputs and outputs, seem likely to conceal or gloss over anytendencies to increasing or decreasing returns between periods ofsimilar rates of operation but different all-out output capabilities.This tendency will be reinforced by the offsetting occurring in puttingtogether the aggregates from data on a myriad of individual unitsexcept in the unlikely event that all, or almost all units, experiencedsimultaneously either strongly increasing or decreasing returns.

(5) Measures of total inputs and output for a dynamic growingeconomy like ours ate likely to exhibit, as a common characteristic,highly correlated growth trends. These correlated growth trends inoutput and inputs will be accompanied by a persistent, rapid timetrend in total productivity of all inputs combined reflecting changesin the intangible contributions to'production already mentioned in-cluding research, education, technological change, improved health,etc. These common time trends complicate the statistical problem ofdetermining quantitatively the functional relationships between inputsand output that constitute the desired aggregate production function.The design of an aggregate production function

In light of the preceding sketch, the required design of a productionfunction incorporating relationships between inputs and outputs canbe laid out in a way that make possible a statistical determination ofthe production coefficients relating each input to aggregate output forthe economy. At this point, and in the following chapter, the over-riding objective of this study must be kept constantly in view since itvitally affects the design and its implementation in chapter III.

The production function is sought as a means of estimating theeconomy's potential output under conditions of sustainable "maximumemployment, production, and purchasing power," and, hence, esti-mating the rate at which this potential has grown in the' past, is grow-ing now, and could grow in the future. This means that'our interest


centers on long-run or secular relationships more than on short-run,cyclical movements.

With this objective in view, characteristics of the desired function,describing production relationships in the economy can be reduced tothese:

(1) It should incorporate measures of as many of the identifiableproductive resources as is possible in light of availability of data,especially-

(a) labor;(b) tangible capital: plant, equipment, etc.;(c) the state of technology and its changes; and(d) other intangibles such as research, health, education, etc.

(2) It should incorporate a procedure for separating changes asso-ciated with cvclical and other short-run fluctuations from changesreflecting secular influences.

(3) Provision should be made to separate changes in output due toshifts in the production function itself in response to changes in tech-niques, etc., from changes in output reflecting increases in the supplyof the productive services of labor and capital.

(4) A procedure is needed for allowing for influences on aggregateoutput and on the productivity of inputs arising solely out of shiftsin demand between goods and services with varying requirementsfor productive resources-i.e., between those with higher or lowerrequirements for capital, and higher or lower requirements for labor.

(5) If possible, specific provision should be made to measure theinfluence of changes in quality of inputs and outputs on the productionfunction.

(6) Since the absolute magnitudes of the measures of inputs andoutputs for the economy as a whole will depend on the particularprice structure used to price inputs and outputs and on various con-ventions of mensuration, these absolute levels will be of little signifi-cance. . Primary attention must center on changes between timeperiods-year to year- and on relative proportions.between measuresin each period. Therefore the form of the function should be chosenso as to operate in terms of rates of change.

(7) If possible, the functional form chosen should be linear or involveonly linear, transformation so as to take advantage of the high speedcomputing possibilities of electronic data processing equipment.This is of special importance in view of the high intercorrelationsbetween the inputs which made it necessary, as will be seen below, torun successive approximations to locate the preferred fit of the formulato the statistical record of past economic performance.

(8) Last, but not least, the formula should be framed to reduce thehigh intercorrelations as far as feasible, especially between.the inputs,or in statistical terms, the independent variables in the function.

In light of these criteria, the search for an aggregate productionfunction, started with a theoretical form that was a variation of, andelaboration upon, the now classic Cobb-Douglas function which islinear in the logarithms. In its original form it was applied to manu-facturing, first to U.S. data, covering various series of years andregions, then to time series for other countries, and then to cross-section data for large numbers of manufacturing industries for eachof several years, here and abroad. In form, the function was:

P=bL' Cl50506--60


Where P was an index of manufacturing production, L was labor input(index of average number of wage earners in manufacturing), C wasthe capital input (index of fixed capital in manufacturing) and b and kwere constants to be found by the classical least squares regressionmethod.

In this form the function assumes that the sum of the exponents isunity, and hence that there existed constant returns to scale. Inlater studies this restriction was removed and more refined variationson data used, with the function assuming the form

P= bLkCiso that k+j could be equal to, less than, or greater than unity. Thestudies of Professor Douglas and his associates, as well as others,tended to arrive at estimates of k+j close to or equal to unity, thoughwith some tendency toward diminishing returns. (28)

This later form of the Cobb-Douglas function was chosen as astarting. point and modified in light of subsequent research resultsand of the changes in availability of data. Five modifications weremade:

(1) Labor input, expressed in man-hours, was split into two com-ponents, first, a secular component (Lp) based on longrun or secularchanges in the rates of participation of the population in the laborforce and secular trends in hours of work and second, a cyclicalcomponent, the ratio of actual labor input to the potential labor

input (Lp)(2) Capital (measured as a gross stock in constant prices) was used

in the form of a ratio of the stock of capital to the potential labor input(K/lp).

(3) The influence of changes in technology on productive efficiencywas captured in part by inserting a new variable, the average age ofthe capital assets surviving in the capital stock in each year (k). Thelower the average age of the capital stock, the closer the productive pro-cess was assumed to approximate the latest, most efficient techniques;the older the average age, the less the stock incorporates the most efli-cient known techniques. This is a measure of qualitative changes-inthe capital stock (K).

(4) A time trend (t) was introduced to measure the influence of allthose intangibles which could not be measured directly. This is aproxy variable, accounting in this case for technical and other changes,or in technical terms for any kind of shift in the production function.

(5) An index (X) was introduced, so constructed as to measure theinfluence of change in demand on the total productivity of the inputs.This index (X) reflects changes in the composition of demand betweenproducts and services requiring varying amounts of labor and capitalper unit.

Inserting these changes in the classic Cobb-Douglas productionfunction, a formula was obtained in the following form, where 0arepresents output:

0O,=A.Lp .[La]a K[ b] kc x d'

The formula was tested against statistical data by least squares, byprocedures outlined along with the results in chapter III. Theformula had to be modified further during the fitting process.

CHAPTER III. THE STATISTICAL ANALYSIS OF OUTPUT

The statistical analysis of the historical record of the output of theU.S. economy and of the major output-determining factors proceededin five stages:

(1) Assembling of historical data on an annual basis for output andeach of the related variables needed for the equation developed inchapter II.

(2) Transforming of the basic variables, where necessary, into theform required in order to fit the equation to the data.

(3) Fitting the equation to the data, using the classic least-squaresregression procedure, making modifications of the equation as testswith the data progressed, and obtaining a final fit by successiveapproximations.

(4) Interpreting the function obtained in economic terms to testits reasonableness in light of economic analysis and other previousrelated studies.

(5) Computing the potential output of the economy for 1909-60,using the derived production function.

The variables and their measurementAs indicated previously, output of the economy is a result of a wide

variety of forces. The growth in the economy's potential output istherefore similarly effected by a range of factors far too large to beincorporated directly in the computations at this time. Fortunately,it is possible to measure output for the economy as a whole, and thetwo major productive factors, labor and capital. As will be seen later,these dominate the rate of growth and cyclical fluctuations to suchan extent that the variables that are not measured directly can berepresented indirectly by a proxy or stand-in. In the historicalanalysis covering the years 1909-58, the influences on our potentialeconomic growth were subjected to statistical analysis making use ofthe following measurements of output and inputs.

(1) Output.-The measure of output is the GNP deflated (adjustedfor changes in prices) to prices prevailing for each of the componentgoods and services in the year 1954. This series is constructed by theNational Income Division, Office of Business Economics, Departmentof Commerce, and published regularly on an annual and quarterlybasis in the '-'Survey of Current Business" (29).

GNP measures the market value of the output of goods and servicesproduced by the Nation's economy before deduction of depreciationcharges and other allowances for business and institutional con-sumption of durable capital goods. The series in real terms, whichwas utilized in this study, reprices this output in terms of prices

19


prevailing on the average during the year 1954. It, therefore, coverschanges in constant dollars of the total purchases of goods and servicesby consumers and Government, net foreign investment, and grossprivate domestic investment, including the change in businessinventory.

(2) Labor.-Labor input has been measured in terms of the totalnumber of man-hours or the product of employment multiplied bythe average hours worked per year per person engaged in production.Two measures of labor input were used. The first of these was aseries on actual labor input in man-hours which represented' theproduct of the total number of persons actually employed multipliedby actual average annual hours worked per person employed (30).

The second measure of labor input was the total man-hours oflabor available for productive activity in the economy, whetheractually employed or not.

It was arrived at by a study of trends in rates of participation inthe labor force of men and women in various age groups, and by astudy of trends in the average annual hours worked-per person en-gaged in production. It was assumed for the historical period (f1909-58) that about 4 percent of the labor force was unemployed when theeconomy was operating at its potential output. Other percentagescould have been assumed without changing the basic historicalanalysis except as to the relative level of the series (31).

(3) The stock of capital.-To measure the supply of capital serv-ices available for use in production an estimate of the gross capitalstock of the private economy prepared by Dr. George Terborgh wasutilized (32).

In this series the gross capital stock represents the value, in con-stant dollars, of all capital assets surviving from past installations atany particular point in time. It is, therefore, gross of depreciation.It includes private plant and equipment in agriculture, mining, manu-facturing, commercial, and similar types of activities, but specificallyexcludes residential structures, inventories, and all Government assets.

(See chart II, p. 21.)These stocks were computed by the application of survival curves

to data on prior installations in constant prices. (See chart. III,p. 22.) Since these curves gave estimated percentages of originalinstallations surviving after given intervals, it is possible to computethe survival at any point from or prior installations and to trace themovement of the survival over any given time (33).

(4) The age of capital.-To measure the degree to which the existingcapital stock incorporates available technology, it was decided to useas one variable in the analysis a computation of the average age ofsurviving capital assets included in 'the above estimate of capitalstock. This also was the work of Dr. Terborgh.

CHART II

Computed Gross Stocks of Business Plant and Equipment at Constant (1959) Prices (Ratio Scale)

Billions of Dollars Billions of Dollars 0

87000 . 1_00 0900 _ - Plont and Equipm ent[T s 2900

400 - 800700- - - | | Plont |700

200 _ . 00

_~~~~~~~~~~~~ln andipmentp nt0

1940 1920 1925 1930 193 1940 945 1950 1955 19600

The 1959 stock includes, of course, a partially estimated installation figure for that year. A mimeographed description.of sources and methods for this and subsequent charts is available on request. t

Source: Capital Goods Review, Nso. 39. t


CHART III

Estimated Percentages of Original Installationsof Plant and Equipment Surviving After the

Periods IndicatedPercent'00

70

40 _ \ \gm.Il

30

TO

60

so~~~~~~~~~se40 10 2 0 4 0 6 0 0 9 0 t 2

These survival curves imply average service lives ofabout 17 years for equipment and 50 years for plant.

Source: Capital Goods Review, No. 39.

The procedure used in computing the capital stock on the basis ofsurvival curves made possible this computation of the age of capital.Since the. survivals are dated by year of origin, it is possible from thecomputation to derive not only the total stock, but its age composi-tion as well. From this, the weighted average age can be com-puted (34).

(5) All other variables.-Because there were a number of importantinfluences which could not be measured directly, the analysis includeda time trend having a constant rate of increase per year. This timetrend is a proxy or stand-in for the many other variables mentionedat the outset, such as changes in managerial skill, technologicalprogress, improvements in the health and education of the laborforce, and so forth. It was found that there was no basis for varyingthis rate from period to period.Three transformations

It was necessary to transform some of the basic information so as toplace three of the terms in the form in which they appear in theequation of the production function. These three transformations

POTENTIAL -.ECONOMIC GROWTH IN THE UNITED STATES 23

produced a cyclical term, a transformation of the capital stock variableand a new variable used to measure the influence on productivity ofchanges in the composition of demand.

(1) The cyclical term.-The central focus, as already indicated, isupon the longrun or secular relationships. On the other hand, theactual historical data contained within themselves movementsrelated to shortrun deviations from the secular movements, including,of course, those relating to the business cycle. It was necessary,therefore, to construct some term that could be used statistically topull out or neutralize the influence on the relationships of theseshortrun and cyclical movements in the historical data.

This was done by the use of the labor inputs. Both a measure ofthe potential labor input (Lp) and a measure of the actual laborinput each year (La) were available. The ratio obtained by divid-ing the actual labor input by the potential labor input, which isdivorced from cyclical and other shortrun movements, yields avariable which fluctuates with the cycle and other short-term devia-tions. It will be noted from the description of these two basicseries above that this ratio represents the actual man-hours workedeach year in the whole economy divided by the potential labor inputin man-hours which could have been worked if the economy had op-erated smoothly in line with the longrun trends in population andlabor force participation. By proxy, this variable also took careof any other cyclical or shortrun fluctuations, since these werevery highly correlated with the ratio of man-hours worked to thepotential man-hours. This cyclical variable is indicated at the end

of the previous chapter -L , and is shown as the top line on chart

IV.(2) The capital transformation.-It was obvious from the beginning

that the stock of capital had grown very rapidly over the last 50 yearsand hence its movements would be highly correlated with the growthof the potential labor force and with the time variable. (See chartIV.) It was decided to transform the capital stock variable bydividing it by the measure of potential labor input giving the term

[ri]_ Thus, taken in combination with the term Lp in the equation,

we have a formulation in which the capital stock has an effect uponoutput independent of increases in the potential labor input, onlyif it rises faster or slower than the potential labor input, so thatthe capital-labor ratio rises Ir falls. This means that the poten-tial labor input (Lp) measures the influence on output of the in-crease in available labor and the associated capital at some constantcapital-labor ratio, and with the average age, or technological state of

FK 1the capital stock, held constant. The capital-labor ratio i-i imeas-

LLpjures the effects on output of a deepening of capital-of a substitutionof capital for labor in production.


CHART IV

GROSS NATIONAL PRODUCT IN CONSTANT bOLLARSAND RELATED VARIABLES, 1909-1958Perceni

130 - 0h

120 La~~~~~~~~~~~~~~~~~~~2

110 -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1

100~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1

19055:A1

K Aein years

- per

60~~~~~~~~~~~~~L

12 0 _ ~~~~~~~~~~~~~~~~~~~~~~~~~GN Pin billons Of

105 - 7500

100

Source, Table 2


(3) Index adjusting for the composition of demand.-Each type ofgoods or service produced in the economy requires at any given pointin time a certain amount of labor and capital for its production. Theamount of each will depend on the state of technology, the characterof the goods or services produced and the ratio of output to capacity.Naturally in historical series of data, changes in the composition ofdemand could bring about changes in the amount of goods and servicesthat could be produced with given amounts of labor and capital if thechange in the aggregate meant a shift toward products and services re-quiring more labor or more capital or less of either or both. In themeasurement of productivity, this so-called mix effect has been widelyrecognized (35).

The procedure employed was to construct an index which measuredthe changes in the amounts of labor and capital required to produce adollar of output of each of the major classes of goods and servicesmeasured in the GNP in constant dollars. The index was constructedby applying a set of capital-output ratios and a set of labor-outputratios to each of a number of categories of goods and services amongthe components of GNP (36). This variable, denoted Xa, is shownon chart IV.

It may be noted that the major influences on the movements of thisindex'over time have been the decline in the relative importance ofagriculture, shifts between goods and services, and shifts betweengovernment and private shares in the total GNP. The index alsoreflects in wartime the extreme shift of demand to fit the requirementsof the war effort. In general, as will be noted on Chart IV, the econ-omy can produce more from a given amount of capital and labor withthe wartime composition of demand than when a more nearly peace-time composition of output is demanded.

TABLE 1.-The variables used in the analysis, and their components, 1909-681

Potential labor input Actual labor input Ratio of

Ratio of gross AverageTime Potential Actual em- Actual actual to Gross tangible age of Mix factor for produc-

Year units average ployment, average potential tangible capital to gross tivity of labor andTotal Potential annual Total including annual labor input capital potential tangible capital

-0.tJ6Mi4fp labor force hours per =E 0 XH. Armed hours per labor input capitalemployee Forces employee

overseas Potent ial Actual

Lp Mp H, La E. H. L0 100 K k XV X.

Billions of Billions of Billions of Dollars perYears man-hours (000) man-hours (000) Percent 1959 dollars man-hour Years 2 1964=100 1954=100

1909-19109 .-- -- - - -1911 .-- - - - - - -

1913 .-- - - - - - -1914 .-- - - - - - -

1916 .-- - - - - - -1917 .-- - - - - - -1918 .-- - - - - - -1919 - - - - - - - -1920 .-- - - - - - -1921 9211122 - - - - - - - -1923 - - - - - - - -1924 .-- - - - - - -1925 .-- - - - - - -1926 .-- - - - - - -1927 - - - - - - - -1928 - - - - - - - -1929 -- - ---. - -1930 --) .- - -- -1931 91

1 932 . .--- - -- - -1933 .-- - - - - - -1934 .-- - - - - - -11135 - - - - - - - -1936---------1937 .-- - - - - - -1938 - - - - - - - -

0 92.841 94.862 96.283 97.654 99.425 101. 166 102. 397 103. 438 104.549 105. 17

10 105.3511 106. 3012 107.9613 109.0514 110.7115 112.6916 114.1717 115. 5918 117.1119 118.5520 119.8721 121.3822 122.2823 123.0824 123. 9325 124.2026 124. 1927 123. 8028 123.6429 123.60

35, 76436, 59637, 19637, 78538, 53539, 27439, 82540,36440, 92141, 28641, 54042,09942, 94243, 56444, 42345, 41546,21146, 99547, 82248, 62449, 37650,21950, 81551, 37051, 95152, 58153, 23453,86054, 43755,063

2,7042,7002, 6962, 6922, 6872,6832,6782,6692,6612, 6542, 6422, 6302,6192,6072, 5962, 5852, 5732, 5622, 9512, 5402, 5292, 5182,5072,4962,4862,4602, 4292,3942,3662,338

94.0696. 5998.48

101. 64102.47100.7099.97

107.06110. 70114. 88107.94107.23

96. 87193. 75111. 57109.46113.46117. 38116. 91118. 04120.36112. 62103. 75

92. 3792. 5492. 6297.74

106.82111.42103.80

34, 78535, 70836, 27437, 34137, 89637, 47537, 66940,12641, 53143, 99842, 31341,49739, 36141,38343, 93843, 31544, 51245, 79545, 90046, 38247, 61145, 46542, 60739, 27439, 61542, 73944, 22447, 07848, 23346, 379

2, 7042, 7052, 7192, 7222, 7042, 6882, 6592, 6682, 6652,6112, 9512, 59842, 4612, 5072, 5442, 5272, 5492, 5632, 5472, 5452, 5282, 4772, 4352, 3922,3362, 1672, 2102, 2692, 3102,238

1.321.812.334.093.06-. 04

-2.423.515. 889.242.45

.88-1. 41-9. 10

.79-2.94-.621. 56

-. 19-. 44

.42-7. 77

-17. 87-33. 23-33. 91-34.09-27.03-15.90-10.97-19. 10

214.7219.9225.9234. 1243. 3252.0258.626s. S273. 928. 6287.9297.33)3. 8309. 4319.2331. 1342. 4354.2366.1377.7390.9403.1409.2408.8405.3402.0400.4401.9406. 5409. 6

2. 3132. 3812. 3462.3972.4472.4912. 5262. 5672. 6202.6702.7332. 7962. 8142. 8372.8742.9382. 9993.0643. 1263.1863.2613.3213. 3473.3213.2703.2373.2253. 2463. 2883.314

14. 5014. 614.7214. 8719.0615.191S. 3739. 5515. 6915.7815. 9716. 1016.2116.3416. 4016. 4316. 5016.4816. 4816. 5016. 4916.4716.7817.3017.9118. 5319. 1919.3119. 4819. 81

04

1:-'

04I0z0

95.72 95.61 295.90 95.87 o96. 07 95.7996.25 16 2796.43 96.2896.61 96.3396.78 96.7096.96 96. 8397. 14 97. 4797.32 97. 5997.50 97 4797.68 98.47017.86 98.10 t98.02 97 8998.11 98.51t98.19 98.60 Z98.29 97.96 ,98.38 98.0498.47 97. 6698. 56 97. 5298.65 98.81 tn98.74 98.13 -3

98.83 98.09 so98.92 97. 59 399.02 96.68 0499.11 99.21 099.20 100. 1099. 29 100. 3099.38 100.4099.47 98.79

1939 --------- 30 123.60 85,8686 2,312 508.653 47, 769 2,272 -13.89 411. 1 3. 326 20.06 99. 56 99. 381940 --------- 31 123. 59 30,306 2,286 113.658 49, 606 2,277 -9.37 419. 2 3.360 20.15 96 991941 - 32 ~~~~~~~~1244 7,14 270 2.42 54,097 2,300 -. 05 422. 3 3.392 20. 11 99. 72 101. 101942 --------- 33 1 25.963 58, 053 2, 254 138. 31 59, 056 2, 342 30. 10 426. 7 3.396 20.40 99.79 102.101943 --------- 34 127. 10 59, 155 2,238 156. 31 (64, 864 2, 410 23.00 425.4 3. 347 20. 80 99.86 1471944 ----- 8.-4-60,202-,222 160.04 66, 020 2,424 24. 89 424.4 3.304 21. 16 99.91 103.161949 -~~~~~- 36 120. 23 61, 010 2,206 150.03 64, 303 2,331 16.09 427.2 3.306 21. 21 99. 98 102:3901946 --------- 17 139.905 61,834 2,191 131. 59 68, 917 2, 232 1.11 439. 3 3.378 29.967 190.09 99.281947-38-10.7-62,30-,176 13932 59,254 2,199 -. 35 490.0 3. 517 20.904 190.09 99. 101948 -~~~~~- 30 131. 80 63,479 2, 193 131.03 60, 216 2, 176 -. 68 482. 7 3. 693 10. 49 100. 16 09.341949 --------- 40 132. 08 64, 409 2, 159 126. 38 68, 702 2, 153 -6. 20 602.7 3.781 19.11 160.21 99. 40919050--------- 41 133. 68 65, 134 2, 138 128. 90 60,491 2, 131 -3. 71 521.3 3.899 18.81 100. 23 10319521--------- 42 134.604 6675,4 2,126 137.690 6,9 2,117 .97 841. 4 3.985 18.48 160.25 160.201952 -43 135.44 60,705 2,113 137.90 ~~~~~~ ~ ~~~~~ ~~65, 264 2,113 1.81 661. 7 4.148 18.12 160.25 160. 301953 --------- 44 139.10 67, 416 2,104 139.79 60. 219 2,096 2.64 582.1 4. 275 17.898 160.28 160. 7019,54 --------- 46 137. 07 683,146 2,6095 134.951 64, 829 2,075 -1. 91 601. 5 4. 388 17. 73 160.28 1600301955 --------- 46 137.02 68,854 2,086 139.01 60,269 2, 098 .81 620.7 4. 901 17.41 160. 30 160 01n11156 -------- 47 19 0 962 207 4.6 67,483 2,090 1.46 6,42. 5 4. 623 17. 21 160. 30 160 101967 -~~~~- 48 140. 38 70, 689 2,069 139. 59 67, 729 2, 061 -. 68 665. 3 4.739 17.09 160.32 099 619 01958 --------- 49 141. 48 71, 538 2,060 123. 11 66, 896 2,067 -6.29 683. 6 4.832 17. 11 100.32 190:' 60

1 For output (O.), see table 2. point to the left one place). In the logarithims, this meant that the characteristic .wasAttention Is drawn to the fact that age of capital, though Presented here In con ven- dropped and the mantissa used without rounding.tioral units, years, was used In the equation in units of decades (moving the decimal 0

H60tv


Fitting the production function to the historical data

The. variables to be used to derive a production function for theAmerican economy for the period 1909-58 now are complete. The sixvariables are shown on chart IV. The equation was fitted by theclassic method of least-squares to obtain the regression of output(Oa) on the other variables, the equation being initially in.the formgiven at the end of chapter II with modifications as will be seen be-low. The data were first translated into logarithms and punched oncards suitable for feeding as input to an IBM 650 electronic computer.

Seven separate runs of the data were made on the computer, eachrun yielding a correlation matrix, regressions between different com-binations of the variables and various statistical measures such asaverages, standard deviations, R2, and a computation of the residualsfor selected equations together with the Durban-Watson statistic totest for autocorrelation.

This procedure could be used only because of the generosity andcooperation of the Bureau of Labor Statistics and the Board ofGovernors of the Federal Reserve System, who made time availableon their IBM 650 computers.

Two difficulties in finding the structural relationship involved inthe aggregate production function have already been noted: a highdegree of correlation of the dependent variable (Oa) and four of thedependent variables (Lp, K/Lp, k, and X) with the time trend (t); andthe aggregation problems arising from combining data for a large num-ber of enterprises with varying characteristics into a simple model forthe economy as a wbole. In addition, the usual complexities asso-ciated with time series of economic data had to be dealt with in theanalysis. As is well known, in time series the data for each year arenot independent observations arising from random samples of the un-known universe but instead values for each year depend on what hap-pened in the preceding year or years. Furthermore, it was clear thatboth the variables and the equations were subject to error so that thestructural parameters could not be determined accurately simply bya direct fit by the least-squares method.

The procedure evolved to overcome these familiar problems was asfollows:

(1) Seven successive runs of the data were made on the IBM 650,with several forms of the equation being fitted on each run.

(2) After each run the coefficients for each variable in each form ofthe equation were tabulated, along with R2 , Durbin-Watson statistic,a's and r's between variables; and charts were prepared showing-

(a) actual and computed values for the more promisingequations;

(b) scatters of residuals from the equations with some or all ofthe variables; and

(c) interrelationships between values of the coefficients in thedifferent equations-particularly the dependence of the coeffi-cients of the other variables on the value of the coefficient fortime (t).

(3) The several values of the coefficients for each variable foundon each run were tested in the light of-

(a) their standard errors;(b) results of other research reported in the literature;

POTENTIAL ECONOMIC GROWTH IN THE UNTITED STATES 29

(c) effects of variations in coefficients of other variables, par-ticularly time (t);

(d) effects of variations in the values of the coefficients on thetime pattern of the residuals; and

(e) the possible economic meaning of the coefficients, and hencetheir reasonableness from viewpoint of economic theory.

(4) The basic data was reexamined in light of the results to deter-mine whether the tests pointed to possible errors or biases in thedata themselves or in the form in which they were specified.

(5) In the light of analysis of each run, specifications were developedfor the next run with two types of modifications each time:

(a) changes in the form of relationship specified for one ormore variables; and

(b) specifications or restrictions as to the values which thecoefficients of one or more of the variables would be allowed toassume.

In all, during the 7 runs over 50 variations in the basic equationwere obtained. Furthermore, after the fourth run, the data werefitted by graphic correlation techniques to test visually what had beenlearned to that point concerning the shape, values, and implicationsof the most probable values of the coefficients. - The equation at thispoint assumed its final form and the final runs merely refined the fitto take care of minor discrepancies revealed by the graphic test.

The final form of the equation, therefore, had to meet three tests.First, the meaningfulness of the regression coefficients, that is, do

the -coefficients- make sense from a priori knowledge of the system?Second, what is the effect of additional variables, or of changes inthe form in which variables are used in the equation, on R2? Is theproportion of the variation in the independent variable (Oa)'explainedby the equation, as measured by R2 , raised enough by each variableto justify the loss of degrees of freedom involved by using it? Third,what is the effect on the standard deviation and the coefficients ofthe other variables of adding each variable to the system? What isthe effect upon the Durban-Watson statistic, that is, on the auto-correlation?

The strictly statistical tests, by themselves, were informative butnot decisive: The lowest RI obtained was .88 and the highest was.9964, with most of the equations having an R2 between .94 and .97.In no case was the Durbin-Watson statistic large enough to warranta belief that autocorrelation had been reduced to insignificant pro-portions. The value of R2 , however, was highly correlated with thevalues of the coefficients of some of the variables-especially thecapital-labor ratio (K/Lp), time (t), and potential labor input (Lp).This made it possible, in combination with the charts showing theinterrelationships of (Lp) and (K/Lp) with (t), to narrow the rangewithin which would fall any acceptable values of the coefficients forthese three variables. Both economic theory and previous studiesprovided bases' for further narrowing the search for acceptableparameters-particularly for these three.

First, it was possible to define narrowly the range within which thecoefficient for time (t) undoubtedly would be found. The runsincluded cases in which the time trend was free to assume any value,was restrained 'to predetermined values, and equations in whichtime was dropped out altogether. From these, it was possible to

30 POTEN-TIAL ECONOMIC GROWTH IN THE UNITED STATES

conclude that the (t) coefficient must be at least as large as .00753 or1.75 percent per year and less than .00966 or 2.25 percent per year.If the time trend was outside this range, the signs of other coefficientscame out reversed or the coefficients assumed nonsense values. Witha high time trend (about 3-4 percent a year), the labor and capitalcoefficients either reversed or became insignificant. At the otherextreme, for example, the coefficients for labor and capital (especiallycapital) became excessively high, indicating an annual rate of returnto capital of almost 2 to 1.

In this study, time (t) is a proxy for the influence on output ofshifts in the production function due to such factors as changes inqualities of inputs and changes in technology. Other studies haveinvestigated this aspect in terms of trends in productivity of laborand capital. The two that are most nearly comparable to our (t) inconcept and measurement are those of Kendrick (30) and Solow (19).Kendrick found that for the private domestic economy, physicaloutput per unit of labor and capital combined (weighted) rose by 2.1percent per year 1919-57 and by 1.3 percent per year 1889-1919.Solow arrived at an upward shift of the production function at about1.5 percent per year for the period 1909-49 with the rate about 0.9to 1.2 percent per year before 1930 and about 1.9 to 2.25 percentper year after that date. His analysis covered the private nonfarmeconomy. Both of these studies used data almost identical withthat used in this study. In our analysis, the acceleration in the rateof change is accounted for largely by changes in the age of capital(k) So that the coefficient for (t) should lie with the range of Kendrick'sand Solow's rates for the period after 1919-or in between 1.9 and2.25 percent which is- indeed the case.

The coefficient of the capital-labor ratio (K/Lp) was sensitive tovalues assumed by time (t) because of the high intercorrelationbetween the two variables (about .96). For time trends within theacceptable range arrived at above, the coefficient of K/Lp assumedvalues between .12 and .57 with values between .3 and .4 for theequations with the highest R2, the most reasonable coefficients forother variables and the most rational pattern of residuals betweenactual and computed outputs (Oa-Om). Solow (19) found a valueof .353 as a coefficient for his capital-labor ratio using an equationform of the Cobb-Douglas type. It seemed reasonable, therefore, inlight of all considerations, to use a coefficient of .35 for the capital-labor ratio (K/Lp), especially as this would be consistent with thedistribution of GNP between property and labor incomes.

With the time trend (t) assumed to lie close to 2 percent per yearand the coefficient for K/Lp fixed at .35, experiments were possiblewith the coefficient of potential labor input (Lp) varied over a rangefrom less than 1 (decreasing returns to scale) to above 1 (increasingreturns to scale). Results of other investigators have been somewhatambiguous but generally pointed to slightly decreasing returns toscale (38). Tests revealed no significant sensitivity of the equationto any reasonable variation in the coefficient of Lp away from 1.0,so it was finally fixed at unity.

With the coefficients of Lp and K/Lp fixed and that of (t) restrictedto a narrow range, it was only necessary to arrive at the optimum

forms for the cyclical component Iralthe capital age variable (k),

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES 31-

and the mix variable (X); after which the optimum fit could be foundby least-squares.- The mix variable (X) by definition has a coefficientof 1 since it is a measure of changes in productivity of labor andcapital combined, assuming all input efficiencies constant but thecomposition of demand variable.

It was clear at an early stage that a linear form for the cyclical[La]

variable -LEa] was not adequate and a nonlinear form had to beadopted. This was parabolic in logs-a result consistent with theeconomic theory of production with fixed supplies of factors, fixedtechnology, fixed mix of demand, and variable rates of use of inputs.

FLal n La FThe final equation therefore used both log L] and log r] asvariables.

The experiments clearly pointed to a nonlinear form also for theage of capital (k) but with a negative curvature in the relevant range.This agreed with expectations. An increase in age of the capitalstock (k) implies that, other things being equal, the technologicalefficiency of the capital stock is reduced below what it would be ifcapital, on the average, were younger and approximated more nearlythe best production techniques known at the time. The curvaturealso was reasonable since the older the capital stock becomes, on theaverage, the smaller would be the proportionate effect on efficiencyof a further aging of the capital stock. Consequently, the age ofcapital entered the final equation as both log k and [log k]2.The final equation

With these points arrived at, the final fit was arrived at on theseventh run.

The final equation chosen on the basis of the many tests was:log Om= -5.43104+log L,+.9104 log (L0/L,)

-3.39[log (LaILp)]2+.35 log (K/Lp)-5.6411 log k+ 10.356 (log k)2 +X+.00884t

N.B.-Om is the predicted value of gross national product and is the equation'sestimate of O.. The relation of 0, to 0, is shown in column 3 of table 2.

N.B.B.-The average age of capital k has been measured in decades whenfitting the equation because of the scaling problem introduced by a squared termif coded input is used.

The equation provided a high degree of explanation of the variationsin output (Oa). The R2 was .9898 and the closeness of the fit canbe seen from the chart V, where the log of the predicted value is plottedvertically against the log of the actual output on the horizontal axis.It will be noted that the dots, representing the various years, areclustered closely around the 45° line which represents a perfectcorrespondence between predicted and actual output. All of thevariables were statistically significant as measured by theirstandarderrors (37).

How sensitive are predicted values to variations in the equation?A test was made by making predictions of potential output for 1959find 1975 using eight different versions of the equation and similarvalues for the inputs. The results showed a maximum deviation fromthe output computed by the final equation equal to about 12 percent,with six of the eight equations staying within 2 percent. Seven of thesixteen predictions fell within 13 percent of the final equations results


CHAPTER V

GROSS NATIONAL PRODUCT IN CONSTANT DOLLARS1909-1958, ACTUAL VS. PREDICTED

Log

2.7

2.6

2.5

2.4

2.3

2.2

2.1

Predicted GNP

21 ~2.2 2.3 2.4 2.5 2.6 2.7ILog Actual GNP

2.0 L2.0

Source: Table 2.

and four were within less than 1 percent. The only predictions whichdeviated by more than 213 percent were computed from two equationsrejected because the time trends were 0 in one and 2.9 percent peryear in the other-values which were both irrational and in disagree-ment with other previous results. Also, in both these equations, thecoefficients of Lp and K/Lp were either statistically insignificant orassumed values which could not be accepted as reasonable on economicgrounds. In particular, the coefficients of K/Lp in the two equationswere extreme-indicating an almost insignificant contribution ofcapital deepening in one case and an excessively high contribution inthe other.


Interpreting the production function in economic termsWhat can be said about economic sense of this statistically derived

production function? It is perhaps useful at the outset to considerthe relative importance of the various factors in explaining changesin output.

(1) The increase in the potential labor input and the associated capital (capital-labor ratio held constant), accounts for between one-quarter and one-third of thechange in potential output.

(2) The change in the ratio of the capital stock to the potential labor inputaccounts for between one-eighth and one-sixth of the change in potential output.

(3) The variation in the age of the capital stock accounts for between 2 and 4percent of the change in potential output.

(4) The many factors represented by the time trend, as a proxy, account forbetween one-half and two-thirds of the total annual increase in potential output.

(5) The other changes in output were determined by changes in the mix orcomposition of demand as between industries with different rates of productivityand by variations in the ratio of actual man-hours to potential man-hours.

To students of the production function, certain economic implica-tions of the present formulation will be readily apparent. Thecoefficient for the potential labor input (Lp) is given at unity. Sincethis term carries with it by implication an associated stock of capitalwith a fixed ratio to the potential labor input and a fixed average ageof the capital stock, this coefficient of unity implies constant returnsto scale. The work of Douglas, Tintner and Solow (38) reached theconclusion that there might be some evidence of a tendency towarddecreasing returns to scale, at least in manufacturing. This studysuggests that if any such tendency prevailed in the economy as awhole over the last half century, then it must have been quite smalland was covered up during this period by the overriding effect oftechnological improvement which would tend to offset any tendencyto diminishing returns (39). Experiments, which varied arbitrarilythe coefficient of Lp above and below 1, gave no indication whatso-ever of improvement of fit to the data.

The cyclical term in the final equation (0.9104 log La-3.39 [logJLLal)

seems reasonable in light of both theory and other empirical research.Its parabolic shape (due to the squared term) implies that at low rates

of operation of the economy (60 to 90 percent for L-) an increase in

inputs will yield a more than proportionate increase in output (Oa),i.e., there will be a cyclical rise in productivity. As operations ap-

proach full employment (100 on the L scale), the cyclical change in

productivity dies out and increases in inputs yield equivalent increasesin output.

When. demand pushes operations to exceptional high rates, ashappened during World War II, output increases do not keep pacewith rising inputs all other variables held constant. This is con-sistent with the fact that at these high rates of operation it is necessaryto bring into use less efficient resources; older, standby plant and equip-ment are put back into use, and less efficient labor is employed.Furthermore, with labor markets exceptionally tight (unemploymentfell below 1 percent at the peak of war production), there is a tendency

34 POTENTIAL ECONOMIC GROWTH mN THE -UNITED STATES-

to hoard labor so that available labor is not used at its most efficientrate.

The value of 0.35 for the coefficient of the capital-labor ratio (K/Lp)appears consistent with some prior studies. For manufacturingDouglas found values for his capital coefficient ranging from 0.10 to0.31 for time series data and from 0.25 to 0.47 for cross-section studies(40). Solow obtains a value of 0.353 for the coefficient of -his capital-labor ratio, when a Cobb-Douglas type function was fitted to data forthe private, nonfarm economy (41). Tintner obtained a coefficientfor capital of 0.332 for the total private economy (42).

The comparison of these other results with our own are not con-clusive in view of the differences in data coverage, definition and formin which the capital variable is introduced into the production function.The previous study closest to this one in its treatment of capital incapital-labor ratio form (Solow's) gives the same result, as alreadyindicated.

That version of Douglas' own functions which comes closest to thisstudy (time series for American manufacturing; series IV) adjustedeach variable for time trends and correlated deviations from thesetrends. This is equivalent to introducing time as an explicit variableas done above (43). In this version Douglas found his capitalcoefficient (j) to be 0.30-a value also close to the 0.35 found for thetotal economy. Douglas, himself, came to the conclusion that thelong-run norm for (j), his capital coefficient, for the period he studied(1899-1922) was probably about 0.34 in manufacturing.

If the compensation of capital roughly corresponded to the con-tribution which an increase in the K/lp ratio made to output (Oa),then with a coefficient of 0.35 for K/Lp, we would expect the propertyshare in GNP on the income side of the national account to be between30 and 40 percent. Depending on the definition of the property shareadopted, its value is in this range, and a rough estimate for the1909-58 period is about 35 percent.

With a K/Lp coefficient of +0.35, we would expect the capitaloutput ratio (K/Oa) to be falling and at a roughly proportionate rateover the long run. Indeed, this is the case.

The influence of the age of capital (k) is inverse and nonlinear asone would expect on theoretical grounds. This variable is an indirectmeasure of the degree to which the capital stock (K) incorporates thelatest technology; when the average age rises, the capital stock is lessmodern, and vice versa. It would be expected, a priori, that anincrease in the average age of the capital stock (k) would be accom-panied by a reduction in the output (Oa) obtained from any givencombination of K and L so the coefficient of k would be negative asit is.

Further, the influence would be expected to be nonlinear. Whenthe average age is low-stock generally very up to date-an increasein the average age would imply a larger proportionate drop in technicalefficiency, than when the average age is quite high and the capitalstock already relatively out moded on the average. The negativeslope of k and its parabolic shape give this result for the relevant rangeof the curve.

The time trend (0.00884) has a rate of rise of 2.07 percent per yearand over the period 1909-58, it accounts for between one-half andtwo-thirds of the rise in output. This result agrees closely with those

POTENTIAL ECONOMIC -GROWTH 1M -THE UNITED- STATES 35

of Kentrick (44), Solow (45), the Bureau of Labor Statistics (46),and the staffs' study of 1957 (47).Potential output: 1909-60

The production function derived above can be used to computewhat the potential output could have been each year if there hadprevailed a state of full use of resources. Two assumptions must bemade. First, a value must be assumed for the cyclical term in the

(La)equation -a. This variable was constructed on the assumption

that Lp, the potential labor input, reflected a constant rate of em-ployment of 96 percent of the labor force and that average annualhours worked followed their trend without short-run, cyclical varia-tions. If we use this as our standard for full employment, La canbe set equal to Lp each year, the cyclical term becomes 1 and can bedropped out. The second assumption is that the potential outputmust reflect history as it had happened up to each year-bygonesmust be bygones. Thus, the Lp, K, and k assume the values in theiractual historical series without adjustment for what might have beenif full use of productive resources had in fact been continually achieved.

Potential output computed on this basis is shown in table 2, p. 37,and on chart VI. The movements are what one would expect-rapid growth during periods of relatively continuous prosperity withminor setbacks, as in the 1920's and 1950's, with actual output (Oa)varying around the potential (Op). On the other hand, the potentialgrew more slowly during the depressed years of the 1930's and output(Oa), fell substantially below potential (Op).

POTENTIALCHART VI

GROSS NATIONAL PRODUCT COMPARED TO ACTUAL1909-1959, AND PROJECTED FOR 1975

( In constant prices )

Index300 r

1909 1920 193

Source: Actual, Deportment of Commerce;Potential, Staff, Joint Economic Committee.

Index

0

>

1:1.

M

0z0

0

0

zH

~3a

H11

H-

January, 1963.

Revised Annual Data and Pfor Ibble 2, page 3

"The Potential Economic

reliminary Quarterly Estimates37, of Study Paper No. 20,Growth in the United States"

(In billions of 1954 dollars]

Year and quarter Actual GNP Potential GRP Oa + 0p

Oa Cp

1947:

1948:

1949:

1950:

1951:

1952:

1953:

1954:

1955:

282.3IIIIIIIV

293.1IIIIIIIV

292.7IIIIIIIV

318.1IIIIIIIV

341.8IIIIIIIV

353.5IIIIIIIV

369.0I.IIIIIIV

363.1E[II

IV392.7

IIIIIIIV

278.4280.4282.9287.2

286.4293.3295.6297.3

291.5290.3295.6293.0

302.7312.0325.6331.6

334.0340.0346.3346.9

349.6349.3352.6362.3

368.9373.2370.2363.9

360.4359.4362.1370.1

382.2389.5397.5401.1

284.3

290.8

303.1

314.1

326.6

340.2

354.6

369.2

386.0

282.2283.5285.0286.5

287.8289.4291.5294.5

298.9301.7304.5307.3

309.7312.5315.5318.7

321.8324.9328.1331.5

335.0338.4341.9345.5

349.1352.7356.4360.1

363.4367.1371.0375.3

379.6383.7388.1392.7

.993

1.008

.960

1.013

1.047

1.039

1.041

.983

1.017

.987

.989.993

1.002

.9951.0131.0141.010

.975.962.971.953

*977.998

1.0321.040

1.0381.0461.0551.046

1.0441.0321.0311.049

1.0571.0581.0391.011

.992.979.976.986

1.0071.0151.0241.021

MORE

(Revised Table 2, p.37, Study Paper No. 20, continued)

(In billions of 1954 dollars]

Year and quarter Actual GUP Potential GNP Oa + OpOa Op

1956:

1957:

1958:

1959:

1960:

1961:

1962:

1963:

1964:

400.9IIIIIIIV

408.6IIIIIIIV

40o1.3IIIIIIIV

428.6IIIIIIIV

440. 2IIIIIIIV

447.9IIIIIIIV

47.1.5PIn:IIIIv

398.8398.9400.2405.5

409.6410.0411.o403.8

393.0395.2402.9413.6

421.7434.o427.6431.1

440.9442.3439.7437.7

433.9443.9450.4463.4

467.4470.8471.6476. ip

IIIIIIIV

404.5

423.3

437.8

456.3

472.8

488.4

508.2

528.4

549.4IIIIIIIV

397.7402.2406.84i1.3

416.7421.4425.6429.5

431.7435.5439.7444.2

449.8454.3458.5462.6

466.5470.7474.9479.0

481.9485.9490.4495.3

500.9505.7510.6515.6

.991

.965

.917

.939

.931

.917

.928

1.003.992.984.986

.983

.973

.966

.940

.910907

.916

.931

.938.955.933.932

.945

.940

.926.914

.900

.914

.918.936

.933

.931

.924

.923

520.7525.8531.0536.2

p=preliminary.

2.


TAELE 2.-Actual, predicted, and potential gross national product in 1954 dollarsfor the United States, 1909-60

[In billions of 1954 dollars]

Actual gross Predicted Potentialnational gross gross

Year product in national G+ 0. national O+- 0,1954 dollars product in product In

0 1954 dollars 1954 dollars0, op

1909 - __-- __-- _-- 104.1 102.2 0.982 101.0 1. 0311910 - _-- __-- __--_-- _106.8 105.6 .989 103. 9 1.0281911 -109. 108.3 .989 100.4 1.0291912---------------- 110.1 112.7 .901 108.9 1.0661913- - 117.0 114.1 .975 111.3 1.0511914 -_------ __-- 112.1 113.7 1.014 114. 5 .9791915 - ___-------- 114.4 113.8 .995 116. 8 .9821916 -_-- __--__--_------ 120.0 122.2 1.018 118. 7 1.0111917 -__--__-- ___-- 120. 5 128. 1 1.063 121.8 .9891918 -- ---------------- 132.9 134.3 1.011 125.0 1.0631019- - __-------- 132.6 129.4 .976 126.7 1.0471920 - _------ ___--_ 125.6 132. 5 1.055 130.4 .9631921 -_--_------___----- 114.9 120.0 1.044 134. 4 .8551922- -_ ------------------ 133.2 131.1 .984 137.9 .9651921 -_----___----- 149. 2 144.6 .969 143. 0 1.0431924-149.0 140.1 .981 149.5 .9971925- -_- ------------------ 161.8 153. 6 .049 154.9 [.0451926 - ------------- 170.8 163.3 .956 161.6 1.05719027- _ - __------ _- 170.5 166.8 .978 168.8 [70121928- - ____----_---- 171.8 172. 6 1.005 175.2 .9811529... ------------- 18L.8 103. 6 [.010 178.5 1.0181930---------------- 104.85 175.1 [.004 190.1 .8651031 --------------- 153.0 158.1 1.033 102. 5 .7951032---------------- 130.1 12. 4 .995 192.2 .6771933---------------- 126.6 130.1 1.028 193.0 .6561934 - ____-- _-- _- 138. 5 131.8 .952 195.2 .7101935 -_-- _--__-- _-- 152.9 148.9 .974 199. 5 .7661936 -__3_--- 173.3 174. 6 1.007 204.1 .8491937---------------- 103.5 169. 7 [1.4 209.7 .8751938 ---------------- 175. 1 171.2 1.901 210.3 .8091039 --- 189.3 102.6 [.017 222.7 .8501940 ---- 205.8 209.1 1.016 229.0 .8091941---------------- 228.1 229. 4 [9015 236.1 1.9081942 -__--_--------__266.9 271.1 1.016 246.0 1.0851943 -_--____---- _:-- 296.7 305.5 1.030 256.9 1.1551944 - _ ------- 317.9 315.9 .994 268.8 1. 1831945 -_----___--_-------_-- 314.0 314.3 1.001 277.1 1. 1331946 -- ---------------- 282.5 280.3 .992 279. 5 [.0111947 -___------___ -- 282.3 280. 6 .994 284.3 .9931948 -____ ------------------ 293.1 290. 7 .992 290.8 1.0081949 -___--__---------- 292. 7 299.9 1.025 303.1 .9661950 -_ 318. 1 303. 7 .955 31i 1 1.0131951- -_--_----___------___- 341. 8 329.5 .964 326.6 1.0471852---------------- 353. 5 346.1 .979 340. 2 1:0391953 -369. 0 364.3 .987 354. 6 1.0411954---------------- 303.1 303.2 [.090 369.2 .9831955- 392. 7 387. 9 6 988 386.0 1.0171956 -____--__--___----_ 400.9 409.0 1.020 404.5 .9911957 -____--___--__--___--_ 408. 3 418.6 1.025 423.3 .9651958 -. _--______--__--____-- 399.0 413.9 1.037 437. 5 .91219-9 -____--_______--_____--_ 425.6p _ _ _ _____ ------ --- 456. lp .gap1960_- _-- _ _____ -------------- 472.6p __-__p._-____

p=preliminary.

CHAPTER IV. POTENTIAL GROWTH: PROSPECTS AND PROBLEMS

The preceding chapters have reviewed the relationship of potentialoutput to the goals of the Employment Act; the problem of analyzingoutput in terms of an aggregate production function; and derivedstatistically the coefficients for such a function. In the present chap-ter, attention turns to the future. How fast could the Americaneconomy's output grow over the next decade or two if the full pro-duction potential for growth which is inherent in the structure of theeconomy is achieved? What are the implications for policy of differentassumptions as to the underlying factors influencing our economicgrowth? What range of possibilities can we reasonably contemplateas a basis for discussion of the issues of public and private economicpolicy?

At the outset it must be recognized that the further ahead weattempt to project our potential for economic growth the more uncer-tain are the resulting estimates and the less likely it is that we canreally effectively apply the results. On the other hand, too shorta period would not allow time for underlying forces to work out theirlonger term consequences. After a review of the various considera-tions it was decided that the year 1975 would be the terminal datefor these projections. It is to be understood that the projections forthe year 1975 are an average of expectations for several years centeredat 1975.

The preparation and analysis of potentials for future growth of theU.S. economy proceeds below in three stages: (1) the alternativeassumptions corresponding to high, medium, and low projections willbe reviewed; (2) the projections themselves will be presented togetherwith analysis of the reasons for deviations, if any, of the future po-tentials from past trends; and (3) the implications of future potentialgrowth rates will be explored, particularly in respect to policy issueswhich may be associated with them.

Alternative assumptions: 1959-75Three alternative projections of potential output and of its rate of

growth to 1975 were prepared; high (labeled A), medium (B), and low(C:). These projections reflect trends of population, participation inthe labor force, unemployment, hours of work, changes in the capitalstock, and the average level of prosperity. These projections, which,of course, are subject to some error, are designed to indicate a realisticrange of potential growth rates that our economy might experienceover the next decade. Table 3, page 40, summarizes these projections.

The projections of population and labor force used in the threealternative projections to 1975 are derived from those prepared by theBureau of the Census, U.S. Department of Commerce (48) and theBureau of Labor Statistics, Department of Labor (49). These weremodified slightly to maintain consistency with the other assumptionsof the three projections.

38


(1) The A or high projection.-Projection A assumes that our eco-nomic affairs are managed in both the private and public area to main-tain a high level of prosperity. While occasionally minor recessionsmight occur, it is assumed that the Nation will not experience a deepand prolonged depression, such as interrupted growth during thedecade of the 1930's. The precise combination of public and privateeconomic policies this projection would require is left unspecified.

Unemployment is assumed to average about 3 percent by the mid-1970's, i.e., about 97 percent of the labor force will be employed in anaverage prosperous year in the 1970's compared to the 96 percentassumed in computing the potential output for 1909-60 in chapterIII. Under such conditions, job opportunities could be expected tobe sufficiently abundant to attract a relatively large proportion of thepopulation into the labor force.

In line with the degree of tightness in labor markets, average annualhours are assumed to decline at a rate of about 0.4 percent per year,slightly slower than the rate of fall over the last half century.

The rate of capital accumulation (rate of growth of the gross capitalstock) is assumed to proceed at a rate of 3.2 percent per year, a ratherconservative estimate of the rate in view of past periods of prosperity(50).

The composition of demand is assumed to follow the historical pat-terns typical of previous periods of strong growth, with allowancefor the effects of continued strong national security demands. Thisimplies about the same share of services in GNP as in 1955-57, reflect-ing a rise in the share for private housing and government and a fallfor consumer services other than housing. The shares of constructionand nondurable goods are assumed to fall moderately, while the shareof durables rises somewhat above the 1957 share.

(2) The B, or medium projection.-The medium projection (B)assumes somewhat more modest success in maintaining continuousmaximum employment, but again assumes no deep, prolonged depres-sion will occur.

Unemployment is assumed to average about 4 percent, the sameassumption used in preparing the historical potential output estimatesin chapter III, shown on chart VI. This means 96 percent ofthe labor force employed on the average. Labor markets, therefore,would be somewhat less tight than under "A" and participation ratesof the population in the labor force would represent a continuationof recent trends.

Average annual hours of work are assumed to decline at a rate ofabout 0.5 percent per year, slightly less than the average rate overthe last half century.

The rate of capital accumulation is assumed to be more modest butstill in line with the assumption that serious depression will be avoided.This means that the gross stock is assumed to rise at 2.7 percent peryear.

The composition of demand is assumed to have little effect onthe growth rate directly through the mix variable, with the rise inthe mix term (Xp) being only 0.001 percent per year.

(3) The C or low projection.-The low (C) projection assumes a con-tinuation of public and private policies in such mixture that therewill be fairly frequent interruptions to growth, inadequate mobilityof capital and labor, and more slack on the average than in each of theother two projections.


Unemployment is expected to average somewhat higher than inthe past best years or about 5 percent. Employment will average,therefore, about 95 percent. Such slack in labor markets is assumedto be accompanied by a slower rate of growth in the labor force asparticipation rates reflect the lower level of job opportunities.

In line with the degree of slackness in labor markets, average annualhours of work are assumed to decline at an average rate of about 0.6percent per year. This is about the average over the past halfcentury-an acceleration over the A and B assumptions consistent withpast experience that reduction in hours of work are more likely underslack conditions than when labor markets are relatively tight.

The rate of capital accumulation is assumed to be lower as industriesare constantly faced with the threat of excess capacity at higherinvestment rates and labor is freely available to substitute for capitalat peak demand periods. This means a rise in gross.stocks at about2.2 percent per year, a low rate compared-to past periods of prosperity.

In all three projections the assumed change in the age of the capitalstock reflects the corresponding rates of growth of capital stock,though the assumptions may tend to underestimate the rate ofdecline in the age of the capital stock tunder the assumed conditions.If this is the case, then a downward bias is imparted to the threeprojections.The alternative projections

The alternative projections, derived by inserting the above assump-tions in the formula for output derived in chapter III, yield a seriesof estimates of potential output of GNP in 1954 dollars for'the year1975. The time trend was not varied between the alternative pro-jections and was the same as derived for the period 1909-58. Therates of.growth implied by these' are' summarized in table 3.

TABLE 3.-Selected indicators of economic growth potentials, 1959-75

[Percent increase per year 2]

Rate of Projected potential growth rates, 1959-76Indicator growth,

1909-58A B C

Total labor force 1.4 1.9 1.7 1.5Total employment, including the Armed Forces. 1.4 31. 9 41. 7 ' 1. 5Average annual hours of work --. 6 -.4 -. 5 -. 6Toa mnhours-.,-- 7-------- 9 1.0 1.2 .9Stock of private plant and equipment in con-

stant prices -2.4 3.2 2. 7 2.2Average age of capital stock -. 3 -.2 -. 1 0Composition of demand-.- .015 .001 -.006Gross national product in constant prices -2.9 -...

From 1959, actual (preliminary estimate) - -5.2 4.7 4.2From 1959 potential - --- 4.6 4.0 3.5

* Some rates of change in this table vary slightly from those given in the similar table 4-1, p. 101 of the"Staff Report on Employment Growth and Price Levels" because of the.incorporation of later data andrefinements of analysis not then available.

2 Computed by compound interest formula, using initial and terminal years.8 Assumes 97 percent of the labor force employed in 1975.d Assumes 96 percent of the labor force employed in 1975.5 Assumes 95 percent of the labor force employed in 1975.

It should be repeated'at this point that the projections for the year1975 do not necessarily assume achievement of maximum economicgrowth each and every year between now and 1975. It is quite

POTENTIAL ECOiN\OMIC GROWTH IN THE UNITED STATES 41

obvious that economic fluctuations or international complications orchanges in policies, public and private, other than assumed, couldincrease or decrease the Nation's production potentials by 1975.Long-run tendencies, incorporated in the production function used tomake these projections, indicate that economic growth at these ratesis a feasible achievement.

Even if these rates are achieved or even exceeded, it does not followthat output in the year 1975 will fall precisely in line with one of theseprojections. Any individual year, such as 1975, may exhibit short-runcharacteristics driving it ahead of or causing it to fall below the long-run rate. In addition, our national economic accounts undoubtedlywill be much improved in scope and accuracy over these 16 years andsuch revisions may appreciably affect the projected levels as well asrates of growth. Finally, it must be reemphasized that these projec-tions assume a stable level of prices-more technically-they assumethat the GNP deflator will remain unchanged at the level of 1954.The projections, therefore, represent changes in real output valued at1954 prices.

A glance at the projected rates of growth in table 3 reveals that thelowest rate of growth (C) is expected to be about 3.5 percent, measuredfrom the potential output calculated for 1959 or about 4.2 percentper year measured from the preliminary estimate of the actual outputfor 1959. This, the lowest of the three projected rates, is signifi-cantly higher than the 50-year average of about 3 percent per year.

The middle or B projection, indicates a projected rate of growth ofpotential output of 4 percent per year, measured from the outputpotential for 1959 or 4.7 percent per year, measured from the pre-liminary estimate of actual output during 1959. The highest projec-tion (A) indicates a possible rate of growth of 4.6 percent per yearmeasured from 1959 potential output levels and about 5.2 percentmeasured from the preliminary estimate of actual output for 1959.Both the A and B projections indicate rates of growth that sub-stantially exceed the average rate over the last 50 years.

Why do these projections, even the lowest, show an acceleration ofthe growth rate compared to the average rate of 3 percent achievedover the past 50 years? The first and foremost reason for this differ-ence is found in one basic assumption used for the projections: namely,there will be no deep, prolonged depression during the next 15 yearssuch as interrupted growth during the preceding 50 years-specifically,the period from 1929 to 1941. This assumption has deep and per-vasive influences on the projections. Increased stability of theeconomy makes a very substantial contribution to an increase in thegrowth rate, affecting the rate of growth of the labor force, the rateof decline in hours of work, the rate of accumulation of capital, thespeed with which new technology is incorporated in actual productionprocesses and the composition of demand. The pervasive influencesof this assumption together with other developments are reflected inthree main factors which account for most of the difference betweenpast and future growth rates:

1. The annual average rate of growth in the total labor force overthe next 15 years is likely to range between 1.5 percent and 1.9 percentper year as compared to an average over the previous 50 years of about1.4 percent. The growth of the population of working age, therefore,


will make possible a somewhat higher rate of growth in the future thanover the past 50 years.

2. The gross stock of private plant and equipment in constant pricesis assumed to grow between -2.2 percent and 3.2 percent per year overthe next 15 years compared to an average of about 2.2 percent per yearover the preceding half century. It is notable that the average rateof increase over the past 50 years has been held down by the fact thatbetween 1929 and 1939 there was very little growth in the stock ofcapital due to the low levels of investment during this decade. Infact, from 1930-31 until 1945 the growth in gross capital stock (K)was barely sufficient to keep pace, on the average, with the rise in thepotential labor input (Lp) so that the capital-labor ratio remainedalmost constant for over a decade. There was a capital widening tokeep up with growth in the labor supply, in other words, but no capitaldeepening to contribute to a rise in the productivity of the system.

3. The average age of the capital stock is assumed to remain con-stant or decline slightly over the next 15 years, whereas the average ageof the capital stock actually increased over the preceding 50 years,reaching a peak during World War II and declining since that time.(See chart IV, p. 24.) The average rate of increase over the entire50-year period was about one half of 1 percent a year, but over mostof the period (1909-45) the rate of increase was slightly over 1 percentper year. Since an increase in the average age of the capital stocktends to retard the rate of growth, and a decline in the average agetends to stimulate the rate of growth, this factor will be a modeststimulant to the economy over the next 15 years, whereas it has beena restrictive influence over most of the preceding half century.

It should be noted that the different assumptions as to the rate ofemployment (or unemployment) have little direct impact on the ratesof growth projected to 1975. In fact, the direct effect would showup in the second or third decimal place, if at all. The differences inthis assumption have their effects indirectly through effects on theother variables: Labor force, hours of work, capital stock, age ofcapital, and composition of demand.

In general, the assumptions chosen for these three projections areconservative. Competent students of the various component factorshave prepared analyses of historical tendencies and future prospectsunder reasonably prosperous conditions which would lead to evenhigher rates of growth. (39) Indeed, no allowance has been made inthese projections for an acceleration in the time trend which hasprevailed over the last 50 years. This time trend of approximately2 percent per year expresses the average influence over the past halfcentury of a wide range of forces which we could not measure directlybut which have strong influences on the growth of the economy.These include the level and progress in educational achievements forthe population, the extent and nature of research and developmentefforts, and any changes in the speed with which improved productionarrangements-other than those requiring significant changes in thecapital stock per man-hour-are introduced throughout the produc-tion processes.

It would not be at all surprising if the accelerated rate of researchand development of recent years, assuming this continues in thefuture, should have some tendency to accelerate the rate of growththrough its impact on the state of technology. Nor would it be sur-


prising if efforts in the educational field should succeed in raising theefficiency of labor and management in the private and public areasof economic activity faster than occurred over the past half centuryduring which efforts in these directions were interrupted for extendedperiods of time by both wars and depression. Finally, it would notbe surprising either if a more pervasive knowledge among manage-ments of the best production practices would raise productivity fasterthan in the past. Even today, in the United States there are verysignificant differences, far wider than seems unavoidable, between thebest practices and those of the least efficient firms in any given lineof production.

Studies of the Bureau of Labor Statistics in connection with itsdirect collection program in the early years following World War IIdeveloped a considerable body of information about individual plantswithin certain industries. For example, when the plants in certainindustries were classified into four groups ranging from the lowest tothe highest in man-hour requirements in unit of output, wide varia-tions showed up. In gray iron foundries, the highest group, the leastefficient, that is, required almost four times as many man-hours perunit of output as the lowest or most efficient group. Furthermore,the lowest group obviously contained some plants which did betterthan the average and some plants in the highest group exceeded thegroup average. The spread, therefore, was even wider than thegroup figures revealed (51).Implications of the projections

These projections have the following implications:(1) Without changing our economic system in any fundamental

way, that is, without instituting elaborate controls or having theGovernment impose a pattern of consumption, and without Govern-ment-imposed, forced high rates of capital accumulation, our economycan grow at a rate as high as 4.6 percent per year. On the other hand,it could prove extremely difficult to achieve rates substantially greaterthan this within our economic system.

(2) If we avoid stumbling into real depression, the rate of growthmay be only as low as 3.5 percent per year, higher than the 50-yearaverage of 3 percent per year which was achieved despite a prolongedinterruption in the 1930's. Thus, there is a considerable range ofpossible growth rates, even within a range of assumptions whichexclude depression and a forced-draft economy.

(3) There is a moderate inherent tendency for the rate of growthof the economy to rise in the coming decade if unemployment canbe held on the average to about 4 percent, or less, of the civilianlabor force. This is due to the increase in the rate of growth in thelabor force and to the fact that the rate of increase in the capitalstock and the decline in the average age of the capital stock would notbe restricted as in the past by long periods of low investment such asoccur in periods of prolonged depression. So long as recessions areneither too frequent nor deep, the rate of accumulation of capital canbe quite favorable to growth.

(4) Our economic growth is within our own control. If the Govern-ment pursues growth-facilitating policies, the economy will expandnear the upper limit of the range. If, on the other hand, the Govern-ment, as a matter of policy, sacrifices economic growth to the pursuit


of other objectives, our economy will perform sluggishly, will add lessto our capacity, and our potential growth will tend to be near thelower limit of the above range or even below.

(5) In recent years, including currently, the output of the economyhas been well below its potential and probably would be in the 1970'sunder the assumptions of the C projection.

From the standpoint of public and private policy, this studyand these projections imply that wide differences in the rate ofgrowth can develop in the future, depending on the degree to whichpublic and private policies contribute: (1) To increased mobility ofFabor and capital to meet the changing demands of our dynamiceconomy; (2) to a rapid rise in educational attainment to keep pacewith requirements of the changing technology associated with higherrates of growth and the high mobility this technological change re-quires; (3) to a high and growing rate of research and developmentexpenditures as a basis for a high rate of technological progress; and(4) to maintenance of such proportions between the growth in invest-ment and in consumption as will not only provide for a high rate ofgrowth of capital stocks and the achievement of a relatively low ageof the stock, but also will produce a growth in final demand forprivate and public consumption sufficient to maintain operations ofthe continually growing capacity at rates of operation which willmaintain private incentives for a high rate of investment and oftechnological progress.

PART II

TECHNICAL MATERIALS

These technical materials supply explanations of terms, sources, andexpansions on details of technique to supplement the discussion inpart I. The sections of these materials below are numbered in se-quence, numbers corresponding to those inserted at appropriate placesthroughout part I.

(1) This prevision of America's future was that of George Tucker,writing in 1912. See Joseph Dorfman, "The Economic Mind inAmerican Civilization," volume II, pages 540-541, the Viking Press,New York, 1946.

(2) This forecast, made in 1872 by a Connecticut doctor, is aninteresting, and indeed curious, example of reason and imaginationapplied to the problem of predicting future economic, social, political,and technological changes. See L. P. Brockett, M.D., "Marvels ThatOur Grandchildren Will See; or One Hundred Years Progress in theFuture," published as part of L. Stebbins, "One Hundred YearsProgress of the United States," Hartford, Conn., 1872.

(3) The Employment Act of 1946, section 2.(4) Ibid.(5) The legislative history of the Employment Act of 1946 was

reviewed by the staff of the Joint Economic Committee and a memo-randum prepared in April 1955 entitled "The Significance -of theWords 'Maximum Employment' as Used in the Employment Act of1946." See hearings on relationship of prices to economic stabilityand growth, Joint Economic Committee, 85th Congress, 2d session(1958), page 1.

(6) During World War II and the transition in 1945-47, a number ofprojections were made of postwar prospects and of the postwar levelsof employment and output consistent with full employment. Amongthese were:Bassie, V. Lewis, "Consumers' Expenditures in War and Transition," Review

of Economic Statistics, August 1946.Cornfield, Jerome, Evans, W. Duane, and Hoffenberg, Marvin, "Full Employ-

ment Patterns 1950," U.S. Department of Labor, Bureau of Labor Statistics,serial No. R1868, reprint from Monthly Labor Review of February and March1942.

Dewhurst, J. Frederic, and associates, "America's Needs and Resources," TheTwentieth Century Fund, Inc., New York, 1947.

George, E. G., in Dun's Review:I. Gross National Product Projections: "The Background and Relation to

Current Issues," March 1945, pp. 9-14.II. Contrasting Estimates; Range and Reasons, May 1945, pp. 9ff.

III. Measuring the Labor Force in 1950, June 1945, pp. 9ff.Goldenweiser, E. A. and Hagen, E. E., "Jobs After the War," Federal Reserve

Bulletin, May 1944.Hagen, Everett E. and Nora B. Kirkpatrick, "The National Output at Full

Employment in 1950," American Economic Review, September 1944.Hart, Alfred G., "Model Building and Fiscal Policy," American Economic

Review, September 1945.45

46 POTENTIAL ECONOMXIC GROWTTH IN THE UNITED STATES

Hauser, Philip L., "W'artime Population Changes and Postwar Prospects,"Journal of Marketing, January 1944, pp. 238-247.

Johnson, Arno H., "Fifty-Seven Million Jobs," address before the Sales ExecutiveClub of New York, Feb. 6, 1945.

Livingston, S. Morris, "Markets After the War," U.S. Department of Commerce,Washington, D.C., March 1943. [Available as S. Doe. 40, 78th Cong., 1st sess.

"Postwar Manpower and Its Capacity to Produce," Survey of Current Busi-ness, U.S. Department of Commerce, April 1943.

"Postwar Income Potentials," in Measuring and Projecting National Income,National Industrial Conference Board, Studies in Business Economics,No. 5, March 1945, pp. 23-27.

Mayer, Joseph, "Postwar National Income," The Brookings Institution, pamphletNo. 55, Washington, D.C., 1944.

Montgomery, D., "Reconversion to What?", Antioch Review, September 1945,v. 5, pp. 309-319.

National Planning Association, "National Budgets for Full Employment," plan-ning pamphlets Nos. 43 and 45, April 1945-study made during spring andsummer of 1944.

Roos, C. F., hearings on S. 380 (Full Employment Act 1945) before a subcommitteeof the Senate Banking and Currency Committee, 1945, pp. 906-912.

Schlotterbeck, Karl T., "Postwar Reemployment," The Brookings Institution,pamphlet No. 54, Washington, 1943.

Slichter, Sumner H., "Jobs After the War," Atlantic Monthly, October 1944.Tucker, Rufus S., "Projections of National Income," National Industrial Con-

ference Board, Business Record, December 1944 and January 1945.U.S. Department of Agriculture, "What Peace Can Mean to American Farmers,"

miscellaneous publications: No. 562, May 1945; No. 570, July 1945; No. 582,October 1945; and No. 589, December 1945.

U.S. Department of Commerce, Bureau of the Census, "Normal Growth of theLabor Force in the United States: 1940 to 1950," prepared by John D. Durand,mimeographed series, P-44, No. 12, June 12, 1944.

Warburton, C., "Normal Production, Income, and Employment, 1945 to 1965,Based on a Statistical Analysis of Past Data." Southern Economic Journal,January 1945, v. 11, pp. 219-245.

Weiler, E. T., "Wartime Savings and Postwar Inflation," Survey of CurrentBusiness, July 1943.

Woytinsky, W. S., "Prospects of Permanent Full Employment," InternationalPostwar Problems, American Labor Conference on International Affairs,September 1944, vol. 1, pp. 485-515.

"Postwar Economic Perspectives," Social Security Bulletin, March 1946,vol. 9, pp. 11, 25; December 1945, vol. 8, pp. 18-29; January 1946, vol. 9,pp. 8-16; and February 1946, vol. 9, pp. 9-16.

(7) Projections of employment, production and purchasing powerneeded to carry out the policy declared in section 2 of the EmploymentAct were made in accordance with section 3(a) of the act in theEconomic Report of the President from 1947 to 1952. These are citedbelow:Date of report: Pages

January 1947 -_ 9-11January 1948 ------------------------------------- 45-47January 19491--__--------_ ------------ 36, 38January 1950 1- 75, 78, 80January 19511- 76-77July 1951 2--------------------------------------- 60-63January 1952 1--------------------------------------------- 113-114

I Contained in the Annual Economic Review, a Report to the President by the Council of EconomicAdvisers. (This review is printed with the Economic Report of the President.)

2 Contained in The Economic Situation at Midyear, a Report to the President by the Council of EconomicAdvisers.

(8) Projections of the levels of employment and production neededto carry out the objectives of the Employment Act and, summariesof the economic outlook based on the annual Economic Report of thePresident, the Joint Economic Committee's hearings, and other


sources, have been made by the staff of the Joint Economic Com-mittee for use of the committee. For these, refer, to Joint EconomicCommittee's Reports on the Economic Report of the President, asfollows:

Page1948 Staff report -11 ff.1950 Staff materials -_ _ _-_ - __-37 ff.1951 Staff materials -26 ff.1952 National defense and the economic outlook for 1953 (fiscal year) - 29 ff.1954 Staff materials -35 ff.1955 Staff materials - 79 ff.1956 Staff materials ------- 77 ff.1957 Staff materials -_- 38 ff.1958 Staff materials -_- - - - - - - - - - 17 ff.1959 Staff materials - 45 ff.

Also the following other publications:"The Economic and Political Hazards of an Inflationary Defense Economy,"

(materials prepared by the staff of the Joint Economic Committee), committeeprint, February 1951.

"Inflation Still a Danger," (report of the Joint Economic Committee, togetherwith materials on national defense and the economic outlook prepared by thecommittee staff) (S. Rept. 644), August 1951.

"Sustaining Economic Forces Ahead," (materials prepared for the Joint Com-mittee on the Economic Report by the committee staff), committee print,December 1952.

"Potential Economic Growth of the United States During the Next Decade,"(materials prepared for the Joint Economic Committee by the committeestaff), committee print, October 1954.

(9) This was discussed at length by various witnesses and con-tributors to the study by the Joint Economic Committee in 1958,entitled "The Relationship of Prices to Economic Stability andGrowth." See especially the summary of the arguments by BerylSprinkel in his paper "Mai'taining Economic Growth, Stability,and Stable Prices," in the commentaries submitted by economistsfrom labor and industry, pages 63 ff.; also, in the compendium ofpapers submitted by panelists appearing before the Joint EconomicCommittee in connection with the same study, see those contributedunder part I, on "Employment Act Objectives and the Stabilizationof Prices" (pp. 1-74).

(10) This was outlined at length by Dr. Edwin G. Nourse in hispaper "Employment Act Objectives and the Stabilization of Prices,"in the study mentioned in note 9 (compendium of papers submitted bypanelists appearing before the Joint Economic Committee, pp. 13-22).

(11) For a discussion of the definition and nature of economicgrowth and its study see:Paper by Grover W. Ensley, entitled "The Employment Act of 1946: The

Dynamics of Public Economic Policy." Compendium of papers submitted. by panelists appearing before the Joint Economic Committee, in connection

with its study of the relationship of prices to economic stability and growth,pages, 1-12. (85th Cong., 2d sess.)

Goldsmith, Raymond W., "The Comparative Study of Economic Growth andStructure," National Bureau of Economic Research 1959.

"Staff Report on Employment Growth, and Price I&evels," prepared by JointEconomic Committee staff, especially chapter II, pages 33-34. (86th Cong.,1st sess., December 1959).

(12) Perhaps the most provocative and widely discussed recentessay based on the distinction between an increase in material goodsand services and an increase in welfare was the book by John K.Galbraith, "The Affluent Society," Houghton Mifflin Co., Boston,1958.


(13) The monthly report on employment, labor force, and unem-ployment is based on the monthly current population survey of asample of households. The basic concepts, definitions, and classifica-tion scheme remained unchanged from the survey's inception in 1940until January 1957. There have been a number of changes in sampledesign and procedures.

Civilian labor force data beginning with May 1956 are based on a330-area sample. For January 1954-April 1956 they are based on a230-area sample; for 1946-53 on a 68-area sample; for 1940-45 on asmaller sample; and for 1929-39 on sources other than direct enumera-tion.

Effective January 1957, persons on layoff with definite instructionsto return to work within 30 days of layoff and persons waiting to startnew wage and salary jobs within the following 30 days are classified asunemployed. Such persons had previously been classified as employed(with a job but not at work). The combined total of the groupschanging classification has averaged about 200,000 to 300,000 a monthin recent years. The small number of persons in school during thesurvey week and waiting to start new jobs are classified as not in thelabor force instead of employed, as formerly. Persons waiting to opennew businesses or start new farms within 30 days continue to be classi-fied as employed.

Beginning July 1955, monthly data are for the calendar week endingnearest the 15th of the month; previously, for week containing the 8th.Annual data are averages of monthly figures.

For the years 1940-52, estimating procedures made use of 1940census data; for subsequent years, 1950 census data were used.The effects of this change on the historical comparability of the dataare explained in the Annual Report on the Labor Force, 1954, seriesP-50, No. 59, April 1955, page 12.

These changes have had measurable effects on the magnitudes shownby the survey. For example, for 1957, unemployment was 4.0percent of the civilian labor force on the old definition but 4.3 percentaccording to the new definitions adopted January 1957.

(14) Stanley Lebergott has shown that, although the proportion ofthe population exposed to possible unemployment has risen markedlysince the early years of the 19th century, the average percent of thelabor force unemployed has shown no distinct trend at all. Changesenabling the economy to operate with lower unemployment in propor-tion to the numbers exposed to its threat have fully offset the increasein the proportion of the population exposed to possible unemployment.See hearings, "Study on Employment, Growth, and Price Levels,"part 3, pages 577-585.

(15) The effects of job shifting, labor mobility, changes in theage-sex composition of the labor force, and other factors on unem-ployment rates was examined in two new studies made for the JointEconomic Committee in connection with the current study of em-ployment, growth, and price levels, by the Bureau of Labor Statistics,U.S. Department of Labor. See Study Paper No. 6, "The Extentand Nature of Frictional Unemployment," and No. 23, "Unemploy-ment in Surplus Labor Market Areas," in press, January 1960.

(16) This was not a determination by the staff that 4 percent wasthe percentage consistent with the objectives of the Employment Act.

POTENTIAL ECONOMIUC GROWTH IN THE UNITED STATES 49

Indeed, it would have no authority to make such. a determination.The staff has stated a number of times that this percentage was de-rived from studies of the past history of employment and unemploy-ment of the United States. See, for example, "Potential EconomicGrowth of United States During the Next Decade," opere citato, page6.

(17) Domar, Evsey D., "Essays in the Theory of EconomicGrowth," New York, Oxford University Press, 1957, page 16.

(18) The pioneering work of Prof. Paul H. Douglas, his earlycolleague, Charles W. Cobb, and his other associates in his work onthe production function was incorporated in a long series of journalarticles and in his book on wages. The first of these was: Cobb, C. W.,and Douglas, Paul H., "A Theory of Production," American Eco-nomic Review, supplement, volume XVIII, March 1928, pages139-165.

The results were incorporated in Professor Douglas' book on wagesin 1934 and later work in a further series of articles. This workwas summed up and evaluated in his presidential address before theAmerican Economic Association at Chicago, Ill., December 29, 1947,entitled "Are There Laws of Production?" The most convenientsource for his work on this problem is the reprint of his book on wages:"The Theory of Wages," by Paul H. Douglas, incorporating a reprintof the article "Are There Laws of Production?", Augustus M. Kelley,New York, N.Y., 1957.

(19) See:Gt Tintner, "A Note on the Derivation of Production Functions from Farm

Records," Econometrica, volume 12 (1944), pages 26 ff.and 0. H. Brownlee, "Production Functions Derived From Farm

Records," Journal of Farm Economics, volume 26 (1944), pages 566 ff.C. G. Hildreth, "A Study of Production Functions From Farm Record Data"(unpublished thesis, Ames, Iowa, 1947).W. H. Nichols, "Labor Productivity Functions in Meat Packing," Chicago, 1948.M. J. J. Verhulst, "The Pure Theory of Production Applied to the French Gas

Industry," Econometrica, volume 6 (1948), pages 295 ff.E. 0. Heady, "Production Functions From a Random Sample of Farms," Journal

of Farm Economics, volume 28 (1946), pages 989 ff.W. W. Leontief, "Introduction to a Theory of the Internal Structure of Functional

Relationships," Econometrica, volume 15 (1947), pages 361 ff.Robert M. Solow, "Technical Change and the Aggregate Production Function"

in the Review of Economics and Statistics, August 1957, volume XXXIX,No. 3, pages 312-320.

(20) On linear programing, see:Robert Dorfman, Paul A. Samuelson, and Robert M. Solow, "Linear Programing

and Economic Analysis," New York: McGraw-Hill Co., Inc., 1958T. C. Koopmans (ed.), "Activity Analysis of Production and Allocation," John

Wiley & Sons, Inc., New York, 1951.Robert Solow, "On the Structure of Linear Models," Econometrica, volume 20

(1952), pages. 29 ff.

(21) On input-output, see, for example:Oskar Morgenstern (ed.), "Economic Activity Analysis," John Wiley & Sons,

Inc., New York, 1954.Netherlands Economic Institute, "Input-output Relations," Proceedings of a

Conference on Inter-industrial Relations Held at Driebergen, Holland, 1953,H. E. Stenfort Kroese N. V., Leyden, 1953.

Conference on Research in Income and Wealth, "Input-Output Analysis; AnAppraisal," Studies in Income and Wealth, volume 18, Princeton UniversityPress, Princeton, N.J., 1955.


W. D. Evans and M. Hoffenberg, "The Interindustry Relations Study for 1947,"The Review of Economics and Statistics, volume 34 (1952), pages 97 ff.

Wassily W. Leontief, "The Structure of American Economy, 1919-1939," 2ded., Oxford University Press, New York, 1951.

* and others, "Studies in the Structure of the American Economy," OxfordUniversity Press, New York, 1953.

(22) For critical analyses of production functions, see:M. Bronfenbrener, "Production Functions," Econometrica, volume 12 (1944),

pages 35 ff.D. Durand, "Some Thoughts on Mlarginal Productivity, With Special Reference

to Professor Douglas' analysis," Journal of Political Economy, volume 45 (1937),pages 740 ff.

J. Marschak and W. H. Andrews, "Random Simultaneous Equations and theTheory of Production," Econometrica, volume 12 (1944), pages 143 ff.

H. Menderhousen, "On the Significance of Professor Douglas! Production Func-tion," Econometrica, volume 6 (1938), pages 143 ff.

Ml. W. Reder, "An Alternative Interpretation of the Cobb-Douglas Functions,"Econometrica, volume 11 (1943), pages 259 ff.

E. Schneider, "Theorie der Produktion" (Vienna, 1934).R. G. D. Allen, "Mathematical Analysis for Economists," London, 1938, pages

502 ff.S. Carlson, "A Study in the Pure Theory of Production," London, 1939.P. H. Wicksteed, "The Coordination of the Laws of Distribution" (reprint),

London, 1932.Burgess Cameron, "The Determination of Production," Cambridge University,

1954.Francis Seton, "Production Functions in Soviet Industry," American Economic

Review; Papers and Proceedings, volume 49 (May 1959), No. 2, pages 1-14,.W. P. Hogan, "The Limitations of Capital Coefficients: A Comment," American

Economic Review, volume 49 (March 1959), No. 1, pages 138 ff.Irma Adelman, "Some Observations on Full Employment Versus Full Capacity,"

American Economic Review, volume 46 (June 1956), No. 3, pages 412 ff.D. Hamberg, "Production Functions, Innovations, and Economic Growth,"

Journal of Political Economy, volume LXVII (June 1959), No. 3, page 228 ff.

(23) There is an extensive literature on the definition of measure-ment of capacity. In recent years, attempts at constructing sta-tistical indicators of capacity, or of changes in capacity, have broughtabout renewed discussion of some of these points in a more practicalsetting. These include the series of surveys of manufacturing ca-pacity made by the Department of Economics of the McGraw-HillPublishing Co. in connection with their annual survey of businessplans for capital expenditures. See particularly their checkup onmanufacturing capacity in connection with the survey in the fall of1958, dated October 6, 1958; the discussion by Sanford S. Parkerand his associates of Fortune magazine in their September 1958issue in an article entitled "How Much Over-capacity in U.S. Manu-facturing?", and his talk before the American Statistical Association,December 10, 1958; and the paper by William F. Butler, entitled"Capacity Utilization and the Rate of Profitability in Manufactur-ing,"i American Economic Review, proceedings, May 1958, volumeXLVIII, No. 2, pages 239-248. Dr. George Teborgh has alsoconsidered this capacity problem and some of his work is presented in"Capital Goods Review," published by Machinery and AlliedProducts Institute. See particularly No. 39, September 1959, andNo. 22, May 1955.

(24) See Paul H. Douglas, "Are There Laws of Production?", andhis other works as cited above in technical note No. 15. Also GerhardTintner, "Econometrics," John Wiley & Sons, Inc., New York, 1952,particularly pages 51-53.


(25) See Tintner, opere citato, pages 53, 55-56, 91-132, 303-304,and other studies cited in his notes.

(26) See Tintner, opere citato, pages 134-143; Robert M. Solow,"Technical Change and the Aggregate Production Function" in TheReview of Economics and Statistics, August 1957, volume XXXIX,No. 3, pages 312-320.

(27) For a convenient survey of the theory of production and pro-duction functions, see Paul H. Douglas, opere citato, and Sune Carlson,"A Study on the Pure Theory of Production," Kelly & Millman, Inc.,1956.

(28) Douglas, opere citato the reprint of his address, "Are ThereLaws of Production?"

(29) The series used was taken from "U.S. Income and Output,"a supplement to the Survey of Current Business, table I-2, pages118-119, and table I-16, pages 138-139.

(30) For employment and hours of work, the figures used werepreliminary data prepared by Dr. John Kendrick in his study for theNational Bureau of Economic Research entitled "Productivity Trendsin the United States" (in preparation), a summary of which was pre-sented by Dr. Solomon Fabricant in his statement before the JointEconomic Committee at hearings in connection with the Study ofEmployment, Growth, and Price Levels (pt. 2, "Historical and Com-parative Rates of Production, Productivity, and Prices," p. 281).We are indebted to the National Bureau for permission to use thesepreliminary data in our study prior to completion and publicationof Dr. Kendrick's volume.

(24) Derivation of potential labor input (L,).-The potential laborinput variable (L,) measures the total amount of man-hours poten-tially available for economic activity during the calendar year. It is,conceptually speaking, equal to the potential labor force multipliedby the average of the potential annual hours of each employee. Thelabor force was assumed to be 96 percent employed, that is, an arbi-trary level of 4 percent unemployment was postulated for the model.This figure was selected because there was the self-imposed constraintthat the model would be built within the existing institutional frame-work, one characteristic of which is an amount of frictional unemploy-ment. On the basis of past experience, 4 percent seemed to be repre-sentative of unstrained full employment. It is underlined, however,that this figure intends no policy recommendations or value judgments.

For purposes of the model, the figure is unimportant because themathematical technique used-that is, correlation analysis in loga-rithms-turns this percent into a constant that is absorbed in theconstant of the equation without effecting the regression coefficientsor the forecast. With the assumption of a constant level of unem-ployment, movement within the labor input series reduces to changesin the labor force and changes in the average annual hours. Thefinal data used for both of these series is a smoothed aggregation ofindividually derived subseries. The procedure was different for eachseries.

Potential laborforce (M1).-The derivation of a potential labor forcefaces both conceptual and technical problems. On the one handthere is the difficulty of reconciling the pre-1940 definitions of gain-fully employed with the subsequent labor force concept, which itself


has changed even as recently as 1957. Then granting the solutionof this problem there is the difficulty introduced by inaccurate meas-urement particularly in the earlier period and by shifting patternsof employment in several of the age-sex groups.

These problems seemed to call for an indirect derivation usingpopulation figures and participation rates. Available MRLF datawere used in the later period, and decennial census figures with inter-polations covered the earlier years.

The participation rate of each of the age-sex groups in table 4 ofBureau of the Census series P-50, were fitted in a multiple regressionagainst an index of unemployment, armed forces, and time. Theresults proved to be consistent with previous studies in this area andprovided a basis from which to project the growth of the labor force.The most significant changes seemed to be the increasing participa-tion of women and the decreasing participation of men under 20 andover 64 years of age. The trend value of the participation rate de-picting full employment was then applied to the population withineach age-sex group and the resulting aggregation provided a potentiallabor force for the early years which was consistent in concept andlevel with the more reliable recent years. The aggregated series wastied in at 1950 to the trend labor force figures provided by the Bureauof Labor Statistics. See table 1, p. 111, "Hearings on the January1959 Economic Report of the President."

Potential average annual hours (Hp).-A satisfactory mathematicalrepresentation of the changing average annual hours proved to beextremely difficult because of substantial structural and institutionalchanges during the period. The general pattern wvas a gradual de-cline until the thirties, a sharp decline until the late forties and then aslowing down of the decline into the fifties. There are of courseseveral explanations for this behavior. In the early third of theperiod both the general shortening of hours and the shift of laborout of agriculture into the relatively shorter houred industrial occupa-tions account for much of the decline. The major downturn in thethirties, particularly after 1934, seems to come from a combinationof the effects of the depression, minimum age and wage laws, and ofthe increased effectiveness of organized labor. The sharp impact ofthese institutional changes seems to have run its course by the lateforties and the lower rate of decline of the earlier period returns, thistime partially accounted for by increasing proportion of women inthe work force, the added premium of leisure, and longer vacations,among other reasons.

The functional representation of the otherwise logical pattern istroublesome. A constant rate of decline over the entire period, thatis a linear function in logarithms, is scarcely representative of anypart of the period and makes economic nonsense when extrapolated.A second-degree parabola is impossible because the series shows aninflexion point during the thirties. Yet, a cubic parabola, thoughfitting the period under observation satisfactorily, will provide aminimum point and eventually an upturn on extrapolation becauseof the nature of the equation. And, the logistic curve, sometimescalled the Pearl-Reed growth curve, proved too inflexible to fitthe data.

The hurdle was finally overcome by a hand-fitted series for thepotential hours. Essentially this boiled down to making linear inter-


polations over short and economically meaningful periods for hoursin each of three sectors-agriculture, private nonfarm, and govern-ment. This resulted in about a 0.4 percent rate of decline in the mostrecent years which corresponds closely to the rate of decline in theearly years, and a more rapid rate in the 1930's and 1940's.

(32) The estimate of capital stock, prepared by Dr. Terborgh, isthat underlaying Capital Goods Review, No. 39, September 1959,published by Machinery & Allied Products Institute, Washington,

(33) Dr. Terborgh describes the procedure and his results inCapital Goods Review, No. 39, September 1959. He comments onpossible shortcoming of his procedure as follows:

This calculation is subject to at least one serious defect. The same estimatedsurvival curves are used throughout. Even if these curves were correct for assetsinstalled in one period, they would not necessarily be so for the installations ofother periods. There is no reason to believe that mortality rates have held con-stant in the past. Because of this instability, actual changes in stocks must havediffered appreciably from changes computed on the assumption of constancy.

It is difficult to appraise the magnitude of the errors arising from this assump-tion. They may be substantial. We are reasonably sure, however, that theyare not sufficient to vitiate the computed results fundamentally. Though nomore than crude approximations, these results offer a significant indicator ofmajor changes in the stock of productive facilities. Needless to say, they shouldbe read for major changes only.

A further warning is in order. Since our calculations relate to the grand totalof business capital goods-agricultural, industrial, public utility, transportation,commercial, and miscellaneous-extreme care should be exercised in drawinginferences for particular classes or product lines. There have been wide differ-ences from one line to another in past installation and survival rates, and theoverall picture may, therefore, be of limited significance for any one of themtaken singly.

(34) See Capital Goods Review, No. 40, Machinery & AlliedProducts Institute, December 1959. The average age refers to aweighted combination of the Terborgh series for plant and for equip-ment.

(35) The problem of allowing for the influence of changes in thecomposition of demand on productivity and costs was discussed in"Productivity, Prices, and Incomes" (materials prepared for theJoint Economic Committee by the committee staff), committee print,June 1957. See particularly the analysis of effects on share of em-ployee compensation in national income (a related issue), pages49-50, 59-60. See also, hearings on employment, growth, and pricelevels part. 2, testimony of Soloman Fabricant, page 281 and followingpages; Bulletin No. 1249, U.S. Department of Labor, "Trends in Out-put Per Man-Hour in the Private Economy, 1909-58," January 1960,especially pages 12-14; and Study Paper No. 17, "Prices and Costs inManufacturing Industries," by Charles L. Schultze and Joseph L.Tryon.

(36) In the past, two basic techniques have been used, particularlyin the study of productivity, to make allowance in time series for theinfluence of changes in the composition of demand. One of these usedby Kendrick, for example in the study cited in note 30 above, involvescombining the inputs with weights reflecting the relative importanceof each industry oF, as in Kendrick's case, by the average compen-sation. The other technique derives measures, such as measures ofproductivity, for each of a number of components of the gross nationalproduct, then combines the outputs resulting from the component


sectors such as agriculture, private, nonfarm, manufacturing, govern-ment, etc. In this study we constructed instead a so-called mix index(X) making use of a breakdown of GNP by type of product or servicerecently initiated by the Department of Commerce and the input-output technique. First, estimates were prepared, utilizing mainlythe Department of Commerce data on GNP, by type of product foreach year 1909-58. These values were in constant 1954 prices. Thebreakdown was that provided in "United States Income and Output,"A Supplement to the Survey of Current Business, November 1958,table VII-6, page 224. The input- output-table developed by theFederal Government at the Bureau of Labor Statistics for the year1947 was utilized to distribute estimates of man-hours worked in eachof about 50 industries and capital stocks in each of these industries tothe final goods and service accounts in the GNP. The proceduremade use of the table given by Evans and Hoffenberg (note 21 above)showing the direct and indirect deliveries of each of the 50 industriesto each of the number of final demand sectors. The contributions ofeach industry to each of these broad final demand sectors was brokendown into the final categories required for our purposes by inspectionof the basic input-output table. Some rough tests showed that morerefined procedures would not make enough difference to be worthwhileat this point.

With the man-hours and capital stocks distributed from industriesto final goods and service categories, these were then totaled for eachcategory of the gross national product. We then had the total numberof man-hours and the total stock of capital employed in producing theparticular quantity of goods or services produced in each category.Dividing the man-hours by the gross national product in each categorygave a labor-output coefficient and division of the capital stock bythe output gave a capital-output coefficient for each category of GNP.

These two sets of labor and capital ratios were used as weights incombination with the annual estimates of GNP by categories of goodsand services to derive an index with 1954 equal to 100. Since thisindex used the changing composition of demand for each year at aconstant set of labor-output and capital-output ratios, the resultingindex expressed the change in the output which the system is capableof generating each year because of changes in the mix of demand butassuming that the efficiency with which inputs were used would remainconstant throughout all years.

Potential mix index (Xv) was computed by fitting a trend throughthe actual index for the individual years. In both the index of actualmix (Xa) and the index of potential mix (X,) the labor and capitalcomponents were combined with changing weights based essentiallyon those used by Kendrick. See note 30 above.

POTENTIAL ECONOMIC GROWTH- mT THE UNITED STATES 55

The GNP categories and the corresponding labor and capital co-efficients are as follows:

Capital per Labor man-GNP category dollar of hours per

output dollar ofoutput

Services:Government gross national product - -0 0.478Other - -1.3 .404Net exports ----------------------------------------------- 2.71 0Blousing-}-------------------------------- 4.807 { 'O ther consum ption ----------------------------------------------------- 4

Construction-- 1.205 .650Nondurables:

Consumers ------------------------------ 1.422 .530Government - -2.317Net exports - -8.196-Change in business inventories - -1. 534

Durables:Consumers -- 5. 345 .476Government - -1.322Not exports - -2.502Change in business inventories - -1.335Producer - -1.02

(37) The coefficients and their standard errors were:Variable

Lazlog z-

[log l ]log k

_ _2

log k[log k]

t

Coefficient

+. 9104

-3. 39

-5. 6411

+10. 356

+. 00884

Standard error

. 0591

. 58

. 7069

1. 358

.00025

The coefficients of Lp and K/Lp were stipulated on the final run as aresult of the preceding tests. However, their coefficients were sta-tistically significant on those runs where their coefficients came outclose to the final values stipulated on the seventh run.

(38) See Douglas, opere citato, and Solow, opere citato, for dis-cussion of relation of production function to returns to scale.

(39) See, for example, William Fellner, "Trend and Cycles inEconomic Activity," Henry Holt & Co., New York, 1956, chapters8 and 9.

(40) See Professor Douglas' presidential address, reprinted in theKelly reprint of his "Theory of Wages," note (15) above.

(41) Solow, opere citato, page 319.(42) Tintner, opere citato, pages 134-138.(43) See for example, Tintner, opere citato, pages 301, 302.(44) See hearings, part 2, pages 283-346.(45) Solow, opere citato.(46) Bureau of Labor Statistics, Bulletin No. 1249, "Trends in

Output Per Man-Hour in the Private Economy, 1909-58."


(47) See "Productivity, Prices, and Incomes," Joint EconomicCommittee, opere citato.

(48) U.S. Bureau of the Census, series P-25, No. 187, November10, 1958, "Illustrative Projections of the Population of the UnitedStates, by Age and Sex, 1960 to 1980."

(49) U.S. Bureau of Labor Statistics, Bulletin No. 1242, "Popula-tion and Labor Force Projections for the United States, 1960 to 1975."

(50) George Terborgh has prepared projections of installations andgross stocks which are somewhat higher than our assumptions. SeeCapital Goods Review, No. 22, May 1955.

(51) See the speech of Ewan Clague, Commissioner of LaborStatistics, before the Chicago Association of Commerce and Industry,May 26, 1959, entitled "Productivity-What It Is and How It IsMeasured," especially page 6 and chart 2.

0